The wisdom behind limiting divorce (talaaq) to three
Question

                I do not know why Islam does not allow the man to marry his wife again if he has divorced her then he wants to take her back. The Qur’an states that she has to marry another man first, then only after that can the first husband marry her again. That does not seem logical to me; rather I think it is harsh.
Praise be to Allah.
    What the individual must do is obey the commands of Allah, 
    may He be exalted, and be certain that He is the most wise of judges; His 
    command cannot be rejected and His rule cannot be overturned. There is 
    wisdom and goodness in all His rulings, and they are in our best interests.

    “And who is 
    better in judgement than Allah for a people who have firm Faith?”

    [al-Maa’idah 5:50].

    Because He, may He be glorified, is the Creator of His 
    slaves, He knows best what is in their interests. He, may He be glorified, 
    has no need of His slaves, is far above any injustice, and is most merciful 
    to His creation. As He is like that, His rulings must be the ultimate in 
    justice, wisdom and compassion. 

    The individual may know the wisdom behind the commands and 
    prohibitions, or he may be unaware of it, but he is enjoined to obey in all 
    circumstances, because this is the state of the weak slave before the 
    Almighty Lord and Sovereign. If he disputes the wisdom of his Creator (in a 
    particular ruling), he has gone beyond the bounds of faith and true 
    servitude to Allah, as He, may He be exalted, says (interpretation of the 
    meaning):

    “It is not for a 
    believer, man or woman, when Allah and His Messenger have decreed a matter 
    that they should have any option in their decision. And whoever disobeys 
    Allah and His Messenger, he has indeed strayed in a plain error”

    [al-Ahzaab 33:36]

    “But no, by your 
    Lord, they can have no Faith, until they make you (O Muhammad SAW) judge in 
    all disputes between them, and find in themselves no resistance against your 
    decisions, and accept (them) with full submission”

    [an-Nisa’ 4:65]. 

    There is nothing to prevent the individual from asking and 
    looking for the wisdom behind rulings, in order to increase his faith and 
    certainty. 

    The one who ponders the issue of divorce will become certain 
    of the mercy and wisdom of Allah. Divorce is painful and harmful for the 
    woman, hence the Lawgiver is very strict about it and has restricted it so 
    that people will not be heedless about it.

    If the man, every time he divorced his wife, was able to make 
    a new marriage contract with her and take her back, a man might divorce his 
    wife dozens of times, and each time he would be harming her and breaking her 
    heart, then people of goodwill would try to reconcile between them, or the 
    woman might feel sorry for her children, so she goes back to her husband. 
    This is obviously unfair and unjust to her. 

    But if the husband knows that the third divorce will make his 
    wife irrevocably divorced from him, in the sense that he will not be able to 
    take her back until after she has married another man who then dies or 
    divorces her, but he may not die or divorce her, then he would be afraid of 
    divorce and would keep away from it, and he would not resort to it except in 
    cases of necessity or urgent need. In that there is mercy for the wife and 
    protection for the family, and it prevents people being heedless about the 
    matter or toying with it. 

    There is also another kind of wisdom behind it, which is that 
    the man may be hasty in divorcing the first time, then he may regret it and 
    take his wife back. Then if he divorces her a second time, he will be doing 
    so with insight and knowledge. Then if he divorces her a third time, that – 
    in most cases – will indicate that they cannot live a stable life together, 
    so there is no point in carrying on with this miserable life, and perhaps 
    separation will be a relief and mercy for both of them, as Allah, may He be 
    exalted, says (interpretation of the meaning):

    “But if they 
    separate (by divorce), Allah will provide abundance for everyone of them 
    from His Bounty. And Allah is Ever All-Sufficient for His creatures need, 
    All-Wise”

    [an-Nisa’ 4:130]. 

    The scholars have commented on the wisdom behind making 
    divorce three times: 

    At-Taahir ibn ‘Aashoor (may Allah have mercy on him) said: 

    The wisdom behind this great legislation is to deter husbands 
    from taking their wives’ rights lightly and making them like toys in their 
    houses. So the husband is given the first divorce as a mistake, the second 
    as a test and the third as a separation, as the Messenger of Allah 
    (blessings and peace of Allah be upon him) said in the hadeeth about Moosa 
    and al-Khidr: “The first time was due to forgetfulness on the part of Moosa, 
    the second time led to the stipulation of a condition, and the third time 
    was deliberate. Hence al-Khidr said to him after the third time: 
    ‘This is the parting 
    between me and you’ [al-Kahf 18:78].”

    End quote from at-Tahreer wa’t-Tanweer, 
    5/415 

    Ibn al-Humaam al-Hanafi (may Allah have 
    mercy on him) said: He may have false feelings that he does not need her 
    (his wife) any more, or that there is a need to leave her, then this idea 
    may take hold of the individual, but when the divorce takes place, he may 
    regret it and feel distressed and become impatient (to take her back). 
    Therefore Allah, may He be glorified and exalted, ordained that divorce may 
    be done three times, so that he might test himself the first time. Then if 
    the reality of divorce confirms his feelings, he may persist until the 
    ‘iddah ends. Otherwise he can try to redeem the situation by taking her 
    back, then if he again feels as he did the first time and that feeling 
    becomes so overwhelming that he divorces her again, he will have another 
    opportunity to think about it after the second divorce. Then by the time he 
    issues the third divorce, he will be very certain of what he wants to do, 
    and after the third divorce there are no more excuses. 

    End quote from Sharh Fath al-Qadeer, 
    3/465 

    And Allah knows best.