I think we have three main problems:
First, is that we do not understand debate as being a back-and-forth process of responsive positions. A responsive position being a statement to which the opponent can respond. Too many of our 'arguments' these days are based upon moral rights and wrongs, but being that morals are relative these are not responsive positions. And so an issue like abortion ends up as competing moral claims. Murder is wrong vs. choice is right. This is an unresolvable argument. We should reframe arguments into works/doesn't work debates rather than right/wrong debates. So regarding abortion we could work together to develop a program to reduce abortions rather than arguing about whose God is better.
Secondly, civility has been tossed out the window. Or more accurately it has been punched, beaten, kicked, spit on, shot, and set on fire. This isn't just a result of the growing pains of figuring out online discourse, but it also comes directly from elected officials. Not sure what to do about this.
And third, is something which is entirely our own fault. People do not in general demand very much from their elected officials. We do not demand or expect sophisticated answers and we are far too willing to accept very simplistic messaging. We then go out into the world and repeat it so frequently that it becomes an accepted truth despite there never being a single shred of thoughtful reasoning or evidence. As long as we accept it, there is no reason to expect politicians to give anything different. The very first thing we should ever do with any claim is to say, "I don't believe that." Not many people seem to do that.
Of course this all assumes that our politicians are even interested in working for the people rather than their own agendas which I don't think is true at all.