Raph is independant. Leo is the lead type. Raph does not want Leo breathing down his neck 24/7. Raph wants his OWN life.
Leo has to think of the whole clan, their safety and somehow get it thru Raph's thick head that he can't go off on his own, which could endanger the others.
Thats often the basis for every fight.
IE:
"Raph, you can't do this."
"Don't gimme yer crap, I'm gonna do what I wanna. Yer not my father, I don't hafta listen to you."
It goes back & forth until Raph snaps and clobbers Leo, of course Leo often wins. Its always been this way. Actually in the comics today he's mellowed out and they don't fight so much. I guess it got tiring.