you have not shown that that they are lying.
While you are busy demonstrating the facts, your opposition has raced on to the next emotional rhetoric.
The malleable middle, unable to follow your complex claims*, empathizes with the latter and votes accordingly.
"We have to get assault weapons off the streets? Our children are dying out there!"
Well, you could explain that
- the term "assault weapon" is a made-up bit of political nonsense, 'cuz you see what they're talking about is just any semi-automatic rifle with a detachable magazine and a flash suppressor, both which are really pretty harmless unless your a soldier, and they're trying to deliberately confuse you with fully-automatic or select-fire "assault rifles", which look the same but really do function differently, and by this point in the discussion we've lost pretty much anyone because all this technical jargon doesn't make sense to someone who hasn't had time to digest it...
- they're not "on the streets", 'cuz you see while they're kinda badass looking they're really too big and annoying for most thugs to use, and once again we kinda lose the audience because now we're off onto another important tangent that they really don't care about...
- our children aren't dying out there, 'cuz you see ... well allright you should get the point by now that this whole thing is getting kinda wordy and boring ...
...but the mushy middle hears some scary stuff, and is preprogrammed by nature to translate that blurb into "predators...offspring...death" and immediately and instinctively go into a defensive posture which, as any good CQB instructor should tell you, shuts down one's cognitive abstract reasoning ability and goes straight to survival, which in this case looks a lot (unfortunately) like Sarah Brady.
* - Remember also: by definition, half the population has an IQ less than 100. Abstract discussions with lots of numbers may not make much impression on them, while "bad men have guns" does.