Sure it is. He’s been stifled in a position he shouldn’t have taken, and (as a consequence) obsessed with getting his ship back, self-conscious and defensive about realizing he’s not as ready and up-to-date as he’d thought, and angry about it. I didn’t say he’s right to be that way or to take it out on Decker — he’s not, McCoy specifically calls him out on it, and frankly this is probably the biggest reason he needs McCoy there… and he knows it. This is completely believable, given that Kirk’s basically been stewing in not being who/what he used to be and is desperately trying to get back to that.
Compassion has nothing to do with it. Kirk is being a jerk, and more than kinda realizes it. As he gradually starts actually using Decker properly, he starts increasingly coming back from that, till finally by the end he’s no longer nervous prickly potential-Badmiral Kirk, he’s Jim Kirk again.
That’s Kirk’s real story in this film, just as Spock’s realization bringing him back from coldly aloof definitely-not-bitter Kolinahr failure to our Spock again is Spock’s.
And I think without these, TMP really would be the Just Another Adventure/“Changeling” remake a lot of viewers see it as. With them, it’s — to me — a much stronger and more interesting film.