There may be a lot of reasons you are unable to draw your defensive handgun with your strong hand (the normal shooting hand). Obviously, you may have been injured in that hand or arm during the early stages of the criminal attack. However, it is also possible you might be dealing with multiple attackers, and one of them may have grabbed your shooting arm in an attempt to neutralize your response to their attack.
I'm sure that, if you think about it, you can come up with a lot of reasons your strong hand is engaged and cannot quickly access your handgun. For these reasons, it is important for the defensive shooter to learn to draw his handgun with the support hand. Most defensive classes teach a segment on support-hand shooting, but it is equally vital to know how to get the gun out of the holster with your support hand.
How you go about getting the handgun into action depends upon where you carry the defensive handgun and your particular physical build. Some will find it easier to reach across the front of their body, pinning the gun against the body until they can get a shooting grip. For others, it might be better to reach behind the back to make the draw. Either way, it is not going to be a fast proposition. One needs to practice getting a solid grip on the handgun and performing the task as smoothly as possible.
When considering the support-hand draw, one quickly realizes that he might have to rethink the position in which he carries his defensive handgun. Also, the type of holster might need to be reconsidered as well. One will quickly find out thumb snaps, safety straps and push-button-retention devices are a real hindrance to the support-hand draw.
The key, of course, to developing the support-hand draw is practice. And, for goodness sakes, do your practice with an unloaded handgun. It also doesn't hurt to practice while standing near a bed or the couch, so your handgun isn't damaged when you drop it, because you are probably going to do just that in the early stages of practice. Also, don't try to catch a falling gun, even if you know it is unloaded.
The support-hand draw is a critical part of your defensive plan. You should be able to shoot with either hand and you should certainly be able to draw with either hand. It may be just the thing to ruin a bad guy's day.