Rocky is a boxer for a new generation. And Mickey is… the old generation.
His face is craggy. His attitude is cranky. He's not physically strong anymore, so he compensates for deteriorated muscles with a nasty attitude—he's a grumpy old man.
He thinks Rocky should retire, and tells him:
MICKEY: The only thing special about you is you never got your nose busted. Well, leave it that way, nice and pretty and what's left of your mind.
Oof. That hurts more than a punch to the nose.
But this is all Mickey's version of tough love. He's angry that Rocky is squandering his potential, and he explains:
MICKEY: I wanna take care of you. I wanna make sure that all this s*** that happened to me doesn't happen to you.
Mickey wants to help Rocky be even better than he was, which is sweet (unlike his salt-and-vinegar pep talks).
The only time Rocky loses his temper is with Mickey, and it's because Rocky knows Mickey is right. In fact, these two have a verbal argument that rivals the movie's final fight with Apollo… although no one has to get their eyelid sliced open.
But remarkably, both men put their differences aside. Rocky agrees to let Mickey become his manager, and Mickey helps Rocky go the distance with the champ. But finally taking off the gloves and fighting it out—verbally—these two are able to put their grudge to rest, and both men grow as a result.