How comes that praising oneself and blame others is unskillful but the teacher of it does? Coming from a closed, probably ill-intended and insulting question, or not, but anyway it's root is actually good to investigate:

How comes that praising oneself is unskillful but the teacher of it does?

There are many places in the teachings, where the Buddha speaks in "glorification" of the "Buddha".


  `(Mv.I.6.7) [11] Upaka the Ājīvaka saw the Blessed One traveling on the road between Gayā and the (place of) Awakening, and on seeing him said to him, “Clear, my friend, are your faculties. Pure your complexion, and bright. On whose account have you gone forth? Who is your teacher? In whose Dhamma do you delight?”
  
  (Mv.I.6.8 ) When this was said, the Blessed One replied to Upaka the Ājīvaka in verses:
  
  “All-vanquishing,
  all-knowing am I,
  with regard to all things,
  unadhering.
  
  All-abandoning,
  released in the ending of craving:
  having fully known on my own,
  to whom should I point as my teacher? [=Dhp 353]
  
  I have no teacher,
  and one like me can’t be found.
  In the world with its devas,
  I have no counterpart.
  
  For I am an arahant in the world;
  I, the unexcelled teacher.
  I, alone, am rightly self-awakened.
  Cooled am I,
  
  To set rolling the wheel of Dhamma
  I go to the city of the Kasis.
  In a world become blind,
  I beat the drum of the Deathless.”
  
  (Mv.I.6.9) “From your claims, my friend, you deserve to be an infinite conqueror.”
  
  “Conquerors are those like me
  who have reached fermentations’ end.
  I’ve conquered evil qualities,
  and so, Upaka, I’m a conqueror.”
  
  When this was said, Upaka said, “May it be so, my friend,” and—shaking his head, taking a side-road—he left.` (The Discussion of the Group of Five)


As this sample shows, such can lead to not benefical situation for one, thinking "how arrogant". 

Lowering others, praising oneself... yet teaching that such is not good...

Broad believe is that the Dhamma teaches generally not so speak about ones good qualities and skills, which seems to be paradox when facing such and lead possible to questions like:


  Was his mind defiled (polluted) with self-conceit; narcistically believing he was better or superior than others? Was the Buddha polluted by the fetter of conceit (mana)? 


So what is that all about with this paradox?

How to explain that his disciples propably blame all others in certain ways and prais just the Buddha and his Dhamma, and his disciples with whole heart?

Just a "Quod licet Iovi, non licet bovi, or how should this statement be understood in a Dhammic way, so to posible do not react foolish like Upaka the Ājīvaka did?

[[Note: This is a gift of Dhamma, not meant for commercial purpose and other low wordily gains by means of trade and exchange]
How comes that praising oneself and blame others is unskillful but the teacher of it does?


The difference is that the teacher is a fully enlightened Buddha - the only one of his kind in this Aeon.

A fully enlightened Buddha has uprooted all defilements. There are absolutely no traces left of any defilements. Its impossible for a Buddha to create Kamma.

What might seem like praise or blame from the perspective of a non-Buddha is vastly and completely different from the perspective of a Buddha.