George Zimmerman is a good example of bad problem

[Straw Man]

45. Rights.

Why does Zimmerman have the right to put a hole in Trayvon Martin, but Trayvon Martin does not have the right to bash an armed aggressor's head into the sidewalk?

The "aggressor" is the person who initiates violence. The court did not determine that this was Zimmerman. You may have beliefs to the contrary, but they have no bearing on the legal issue.

Gun owners are pretty much always allowed the use of deadly force, even if they start a fist fight, then lose, then pull their gun.

That varies from state to state. Florida state law does not allow the aggressor to use deadly force, with two exceptions:

(a) Such force or threat of force is so great that the person reasonably believes that he or she is in imminent danger of death or great bodily harm and that he or she has exhausted every reasonable means to escape such danger other than the use or threatened use of force which is likely to cause death or great bodily harm to the assailant; or
(b) In good faith, the person withdraws from physical contact with the assailant and indicates clearly to the assailant that he or she desires to withdraw and terminate the use or threatened use of force, but the assailant continues or resumes the use or threatened use of force.

--http://www.leg.state.fl.us/statutes/index.cfm?App_mode=Display_Statute&URL=0700-0799/0776/0776.html

In other words, even though you may have initiated the fight, you are not legally obligated to allow the other person to kill you. If you stop fighting and the other does not, you are no longer the aggressor.