The burden of proof is not on Zimmerman, it is on the state. Zimmerman does not have to prove who started the fight. If the prosecution can not prove that he started the fight, then he has performed no criminal act. Massively stupid, yes; criminal, no.
Zimmerman following Martin was legal, even IF it scared Martin. I can follow you all day long, and you have no real (though several practical)legal recourse to stop me. If I do it habitually over several days you do. Zimmerman was stupid to follow Martin, but legally allowed to do so.
The state failed to prove (or even effectively insinuate) that Zimmerman initiated the physical altercation with Martin. Physical trauma (none to Martin, except on his hands, facial trauma, broken nose, lacerations to the back of his head) indicates that Martin was the aggressor (he inflicted but did not receive damage). If Martin was the aggressor, then Zimmerman was defending himself. The only argument you can make at that point is that Zimmerman shouldn't have ben in fear for his life (thus allowed to use lethal force). If you want to try that argument, I suggest you find someone to break your nose and bounce your head on concrete, I believe your opinion will change.
1 final point. Reverse the outcome. Imagine all the physical evidence the same, but Martin is alive and Zimmerman dead. His story is that some guy was following him, wouldn't talk to him, suddenly he was attacked (Mr Martin, where are your injuries? Here on my knuckles, he never managed to lay a hand on me. How could he attack you if he never laid a hand on you?) and had to kill his attacker. You think THAT would stand up in court?