Is Udhiyah Obligatory?
Question

Could you please present some evidence that udhiyah is Sunnah and not obligatory? What about the hadith “Whoever can afford it but does not offer a sacrifice, let him not come near our prayer-place.” [Ibn Majah, hadith no. 3123]?
Praise be to Allah.Is udhiyah obligatory or sunnah?
Concerning this issue there is a well-known difference of opinion among the scholars (may Allah have mercy on them). Most of the scholars are of the view that udhiyah is Sunnah, and is not obligatory.
The Hanafis and Imam Ahmad, according to one report, which is also the view favoured by Ibn Taymiyah, are of the view that it is obligatory for one who can afford it.
Ibn Qudamah (may Allah have mercy on him) said:
“The majority of scholars are of the view that udhiyah is a confirmed Sunnah and is not obligatory.
That was narrated from Abu Bakr, ‘Umar, Bilal and Abu Mas'ud al-Badri (may Allah be pleased with them). It was also the view of Suwayd ibn Ghafalah, Sa‘id ibn al-Musayyab, ‘Alqamah, al-Aswad, ‘Ata, ash-Shafi'i, Ishaq, Abu Thawr, and Ibn al-Mundhir. Rabi‘ah, Malik, ath-Thawri, al-Awza‘i, al-Layth, and Abu Hanifah said: It is obligatory, because of the report narrated by Abu Hurayrah, according to which the Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever can afford it but does not offer a sacrifice, let him not come near our prayer-place.” And it was narrated from Mikhnaf ibn Sulaym that the Prophet (blessings and peace of Allah be upon him) said: “O people, each household, each year, must offer a sacrifice (udhiyah) and an ‘atirah [a sacrifice that was offered during Rajab in the pre-Islamic period].”
There is also the report narrated by ad-Daraqutni, with his isnad from Ibn 'Abbas, that the Prophet (blessings and peace of Allah be upon him) said: “There are three things that are obligatory for me, but for you they are optional.” According to another report, they are: “Witr, the sacrifice (udhiyah) and the two (Sunnah) rak‘ahs of Fajr.”
And the Prophet (blessings and peace of Allah be upon him) said:” Whoever wants to offer the udhiyah , when the first ten days of Dhu’l-Hijjah begin, let him not remove anything of his hair or skin.” (Narrated by Muslim) Offering the udhiyah is connected to wanting to do it, but that which is obligatory cannot be connected to wanting to do it.” (Al-Mughni, 11/95)
Evidence of those who argue that udhiyah is obligatory
Each group of scholars quoted several things as evidence for its view, but the evidence is not free of some reservations concerning its isnads, or some dispute concerning its interpretation. We will limit our discussion to the most significant of the marfu‘ hadiths.

With regard to the first hadith quoted by those who say that it is obligatory:

It is the hadith of Abu Hurayrah, according to which the Prophet (blessings and peace of Allah be upon him) said: “Whoever can afford it but does not offer a sacrifice, let him not come near our prayer-place.” [Ibn Majah, hadith no. 3123]
Some of the leading scholars of hadith did not accept that it is marfu‘ (attributed to the Prophet (blessings and peace of Allah be upon him)), and they judged it to be the words of Abu Hurayrah, not the words of the Prophet (blessings and peace of Allah be upon him).
Al-Bayhaqi said in his Sunan (9/260): 
“I heard that Abu ‘Isa at-Tirmidhi said: With regard to the hadith narrated by Abu Hurayrah, it may be soundly attributed to him, but it is mawquf (that is, it is the words of the Sahabi and cannot be attributed to the Prophet (blessings and peace of Allah be upon him)). It was narrated by Ja‘far ibn Rabi‘ah and others from ‘Abd ar-Rahman al-A‘raj from Abu Hurayrah as a mawquf report.”
Al-Hafiz Ibn Hajar said: 
“It was narrated by Ibn Majah and Ahmad, and its men are thiqat, but there is a difference of opinion as to whether it is marfu‘ or mawquf. The view that it is mawquf is more likely to be correct. This was stated by at-Tahhawi and others. Moreover, it does not clearly state that (offering the udhiyah) is obligatory.” (Fath al-Bari 912/98)
The view that it is mawquf was deemed more likely to be correct by Ibn ‘Abd al-Barr, ‘Abd al-Haqq in al-Ahkam al-Wusta (4/127), al-Mundhiri in at-Targhib wa't-Tarhib, Ibn ‘Abd al-Hadi in at-Tanqih (2/498). See: Hashiyat Muhaqqiqi Sunan Ibn Majah (4/303).

The second hadith is the hadith of Abu Ramlah from Mikhnaf ibn Sulaym, in a marfu‘ report: “O people, each household, each year, must offer a sacrifice (udhiyah) and an ‘atirah.” Narrated by Abu Dawud (2788), at-Tirmidhi (1596), Ibn Majah (3125).

The ‘atirah was a sacrifice that they used to offer during Rajab [before Islam]. It was also known as ar-Rajabiyyah.
A number of scholars classed this report as da‘if (weak), because Abu Ramlah, whose name was ‘Amir, is unknown.
Al-Khattabi said: “This hadith is da‘if, and Abu Ramlah is unknown.” (Ma'alim al-Sunan, 2/226).
Az-Zayla‘i said: 
“‘Abd al-Haqq said: Its isnad is da‘if. Ibn al-Qattan said: The problem with it is the fact that Abu Ramlah, whose name was ‘Amir, is unknown; he is only known for this report, which was reported from him by Ibn ‘Awn.” (Nasb ar-Rayah, 4/112)
Evidence of those who argue that udhiyah is sunnah 
With regard to those who say that it is recommended, they quoted as evidence a number of marfu‘ hadiths, the most important of which are the two hadiths that were quoted by Ibn Qudamah (may Allah have mercy on him).

The first hadith is the hadith of Ibn 'Abbas, according to which the Messenger of Allah (blessings and peace of Allah be upon him) said: “There are three things that are obligatory for me, but for you they are optional: Witr, the sacrifice (udhiyah) and Duha prayer.” (Narrated by Ahmad (2050) and al-Bayhaqi (2/467)

This hadith was classed as da‘if by a number of earlier and later leading scholars of hadith. Ibn Hajar (may Allah have mercy on him) said:
“The reason for its being classed as da‘if is that it was narrated by Abu Janab al-Kalbi, from ‘Ikrimah. But Abu Janab is da‘if and mudallis [i.e., he engaged in tadlis, which is when a narrator narrates a hadith that he did not hear directly from his shaykh, without mentioning the name of the third party from whom he did hear it, using wording that may or may not give the impression that he heard it directly], and he narrated by saying ‘an (from) [this is weaker than saying “So and So told me” and the like, especially on the part of one who is mudallis]. The leading scholars such as Ahmad, al-Bayhaqi, Ibn as-Salah, Ibn al-Jawzi, an-Nawawi and others deemed this hadith to be da‘if. End quote from al-Talkhis al-Habir (2/45). See also (2/258).
The second hadith is the hadith of Umm Salamah, according to which the Prophet (blessings and peace of Allah be upon him) said: “When the ten (days of Dhu’l-Hijjah) begin, and one of you wants to offer a sacrifice (udhiyah), he should not remove anything from his hair or nails.” (Narrated by Muslim, 1977)
Imam ash-Shaf‘i said: 
“This indicates that the udhiyah is not obligatory, because the Prophet (blessings and peace of Allah be upon him) said: “and [he] wants”, so he connected it to his wanting to do it. If it were obligatory, he would have said: let him not remove anything from his hair until he offers the udhiyah.” (Al-Majmu‘, 8/386)
But this deduction is subject to further discussion, because making something dependent upon wanting to do it does not prove that it is not obligatory.
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said:
“In my view, making it dependent upon wanting to do it does not rule out its being obligatory, if evidence to that effect is proven. The Prophet (blessings and peace of Allah be upon him) said concerning the miqats: “They are for them and for anyone other than their people who come to them, wanting to perform Hajj and ‘Umrah.” This does not mean that Hajj and ‘Umrah are not obligatory, based on other evidence. … The udhiyah is not obligatory for one who cannot afford it, so he does not want or intend to do it. So in this regard it is valid to divide people into those who want or intend to do it and those who do not, based on whether they can afford it or not.” (Ahkam al-Udhiyah wa’dh-Dhakah, p. 47)
Conclusion
There are some reservations about the hadiths which say that the udhiyah is obligatory, although some of the scholars classed some of these hadiths as hasan. The same applies to the hadiths which state that it is recommended; in fact, in terms of their isnads, they are more weak.
Hence Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said, at the end of his lengthy essay Ahkam al-Udhiyah wa’dh-Dhakah: “These are the opinions of the scholars and the evidence that they give. We have quoted them in order to highlight the status and importance of the udhiyah in Islam. The evidence for each view is almost equal in strength, and the prudent approach dictates that one should not neglect to do it if one can afford it, because of what it involves of venerating and remembering Allah, and discharging one’s obligation with certainty.”
Support of the view that udhiyah is not obligatory
There are two things that support the view that the udhiyah is not obligatory:

The principle that things are not obligatory unless proven otherwise: so long as there is no sound proof of it being obligatory, then the basic principle is that it is not obligatory.

Shaykh Ibn Baz said: 
“The ruling on the udhiyah is that it is Sunnah if one can afford it, but it is not obligatory, because the Prophet (blessings and peace of Allah be upon him) used to sacrifice two rams that were white speckled with black, and during his lifetime and after his death (blessings and peace of Allah be upon him), the Sahabah also used to offer the udhiyah, as the Muslims continued to do after their time, and there is no report in the shar‘i evidence to suggest that the udhiyah is obligatory. The view that it is obligatory is a weak view.” (Majmu‘ Fatawa Ibn Baz, 18/36)

The sahih reports that were narrated from the Sahabah.

It was narrated in sahih reports from Abu Bakr, ‘Umar and others that they did not offer the udhiyah, because they did not want the people to think that it was obligatory.
Al-Bayhaqi narrated in Ma‘rifat as-Sunan wa’l-Athar (14/16, 18893) from Abu Sarihah who said: I lived during the time of Abu Bakr and ‘Umar; they were neighbours of mine, and they did not offer the udhiyah.
Al-Bayhaqi said, after quoting this: “It was narrated to us in the books of as-Sunan, from the hadith of Sufyan ibn Sa‘id ath-Thawri, from his father, and the hadith of Mutarrif and Isma‘il, from ash-Sha‘bi, and in some of their reports it says: That was because they did not want to be taken as an example [and think that the udhiyah was obligatory]. (See also: as-Sunan al-Kubra, 9/444)
An-Nawawi said in al-Majmu‘ (8/383): “With regard to the report which speaks about Abu Bakr and ‘Umar (may Allah be pleased with them), it was narrated by al-Bayhaqi and others with a hasan isnad.”
Al-Haythami said: It was narrated by at-Tabarani in al-Kabir and its men are the men of as-Sahih. End quote from Majmu‘ az-Zawaid (4/18). It was classed as sahih by al-Albani in al-Irwa (4/354).
Al-Bayhaqi (9/445) narrated with his isnad from Abu Mas‘ud al-Ansari (that he said): I refrain from offering the udhiyah even though I can afford it, for fear that my neighbour may think that it is a must for me. (Classed as sahih by al-Albani in al-Irwa)
And Allah knows best.