The thing that someone who has a firm grasp on an issue will often find is that most people on both sides don't actually know what they are talking about.
I think the first time I really realized it was when I was drifting away from my religion of birth, and actually started to listen to atheist people around me. I soon discovered that the only difference between most of them and the religious people I know was the value of $religion variable. For one group it was "God", for the other it was "no God". The thought patterns were exactly the same. Neither of them could actually justify their beliefs.
For example, I personally have a stake in the gun control issue. I'm against "banning assault weapons" because I'm against a bunch of bureaucrats having a chance to define "assault weapon" because last time we gave them a chance they banned a bunch of things that make firearms look scary. Ditto for background checks but to a lesser extent. Existing implementations suck, a lot. The same goes for tougher laws in general, they don't seem to have done much of anything for the positive and there's anecdotal evidence they may be negative (look up some of the pro-gun number crunching exercises f you want an example). Why would I or anyone else who wants to go to the range want to encourage more of this? We see it as the firearm equivalent of security theater.
However people who aren't well informed on the details have had these two carrots danged in front of them as a cure to a problem in our society and they'd be fools not to reach for them when they're framed in that context. Meanwhile they can't be bothered to wonder why anyone wouldn't want these things. After all, some poll says $large_percent of people support $thing, yet they can't be arsed to even wonder why that $small_percent is holding out.
You find this sort of problem on both sides of any controversial issue.