The Five-Fold Path
Splinter taught them: You must know why you fight. Not why you're in this fight, what justifies using your fists and your weapons against someone else's flesh, but why you fight at all, ever. If you do not know this, you lack discipline. You do not control your energy.
The Turtles spend a lot of time reflecting on this, trying to find the Right answer, learning to seek their True answer. Their reasons change as they grow, but over time they each find their own Way, the motivating core that focuses them in training and guides them in real combat.
Leonardo fights from Love. He fights to protect his brothers, his city, the principles to which he is so devoted. He cherishes ninjutsu, and Bushido, too much to see them perverted. He strives for righteousness and superior skill, and some part of him is not yet too jaded to stop hoping his enemies will see the way of honor, and turn from evil.
He fights because he cannot allow such blinded men near his family, where they might poison those he cares about. He leads because he loves his brothers too much to let them stray down a wrong path.
Donatello fights from Duty. He thinks fighting is the resort of the unintelligent or irrational, and he resents being pulled down to that level. At the same time, he recognizes the paradox: his opponents are irrational; he cannot reason with them. His responsibility, then, is to defeat them any way he must. He is no good to anyone dead. He must survive, so he can do the creative work that is so much more meaningful, and of such great value to his family.
He trains because he cannot be a liability. He defends himself because his family needs him alive.
Raphael fights from Fear. He always secretly worries that he is not good enough: that his brothers will abandon him, or that a mistake will cost one of them their lives. But whenever he leaves someone lying on the pavement, it is obvious to all that he is a formidable warrior. No one can question his strength, his ferocity, his skill with a sai. None can doubt his bravery in battle.
He practices ninjutsu because he loves the swell of confidence that comes of being able to do such things. But he fights because he's terrified of losing his family.
Michelangelo fights from Anger. No one would guess, from his easygoing attitude, that this is his centering force. He's confident in his abilities, and he enjoys pushing his luck, but there's a difference between attempting dumb skateboard tricks and going up against someone who is actively trying to kill you. In those moments, everything precious to him is on the line: his life, his family, his integrity of body and freedom of movement. He never agreed to wager these things.
He fights because being threatened infuriates him. He keeps his reason locked away because life is too short for hate.