Plenty of people shoot with their non-dominant hand, including me, strangely enough.
Someone with no firearms experience will not understand the reason for it.
But a right-hand draw is next to impossible ... at least the way Zimmerman stated it happened. Here is a snap from the video showing Zimmerman reenacting the moment he pulls the gun. He claims Martin has reached for his gun now that it has become exposed and Zimmerman has pinned Martins arm with his right arm while he pulls the gun.
To prove how impossible this really is, look where Zimmermans hand can reach while pinning his other arm (representing Martins arm). He cannot reach up to his waist band with his right hand, nor can he really draw a gun up and out of a holster. Now look where Zimmerman puts his hand just a few seconds earlier when he indicates where he wears his holster.
A few items to point out here. First is Zimmermans holster is worn around the back which means Martin could not see it if he was sitting on top of Zimmerman with Zimmermans back on the ground. Second, there is no way to pin the arm and pull the gun as can be seen in this second position where Zimmerman mimics grabbing his holster. Look where his elbow is. This is all fabrication because it is all physically impossible (line of sight to the holster, elbow length and arm motion).
While there are many discrepancies throughout Zimmermans tall tale, some are simply too big to ignore. There is no way GZ could pull his gun as described. On his back with his holster against his hip, his holster inside his waistband, while being pinned by Martin who is supposedly straddling him. This position means Martin's legs are blocking access to GZs waist area, as well as the ground and clothing making it impossible to reach and pull a gun. In this position you cannot pull a gun on a wet and rainy night without leaving some evidence on the gun.
There is almost no Zimmerman blood or DNA on Martin. Martin should be covered with blood or DNA from the punching and from the claimed suffocation attempt. But there is none.
There is no Martin blood or DNA on Zimmerman, which there would be if he was shot while straddling over Zimmerman. Blood would begin to flow and should be all over him.
If Martin was really banging Zimmermans head on concrete, there should be some fractures in the skull. Apparently there are no injuries consistent with multiple hard blows to the head.
Finally, the path of the bullet in Martins body is not possible from the position described, and really is only possible if both men are standing AND Zimmermans arm is extended straight. When you look at the bullet path inside TMs body it is pretty clear that this was not a shot from underneath, which would be at an angle if events transpired as Zimmerman claims.
You cant break the laws of physics/biology/chemistry this is not a fictional world. The crime scene evidence completely destroys Zimmermans story, even before you get to issues like the timeline described vs the timeline recorded on the dispatch call, the lies about why Zimmerman exited the car -- to follow Martin, not to read house numbers which were right in front of him. Basically, nothing beyond the fact he shot Trayvon appears to be true.