It's often clear that one ideological disposition relies on laughably untrue rhetoric more than the other, but on their best days, the left and right both agree on facts, they just disagree on their interpretation of them and what that means we should do.
Debate doesn't work because the idea of the right is to restrict resources to the "deserving" (individualism, tax breaks, etc) and kick around everyone not in the in group. The left says that we can make a more equal society and so we should try to solve our problems by redistributing resources.
This is not a gap you can bridge with logic, it's a fundamentally different moral interpretation of reality. This is sharing vs defending.
EDIT: However, Noam Chomsky gave a very interesting talk about how moral senses develop and change. There is some flexibility in our moral systems. For instance, until like, a year or two ago, casual homophobia was acceptable in public, now it isn't amongst a growing swath of the population. It's kind of fun to look at old Tweets by media personalities and see how much they've changed their positions (something very desirable) either because their beliefs changed or because their audience did.