Gunna take this as Liberal/Conservative as party brand names rather than strict social ideology and you're talking about "the left" more generally.

I think the short answer is empathy. When you dig down to the bottom a lot of the discussion on the left talks about different forms of human needs. A need to feel accepted and loved, desires to exist publicly without fear... It is a radical form of empathy that asks you to put yourself in multiple pairs of shoes and see the world through perspectives you aren't naturally born into. The ultimate aim is to achieve a picture of humanity which is inclusive of the widest possible range of understanding.

In that way "Conservatives" are also people. It is not impossible to empathize with their issues. It takes a lot cognitively to internalize this new data and a lot of the rejection from the right comes not from outright cruelty but a desire for things to be and remain simple and easy. They don't want to stretch themselves and are scared of a world where that is something they are forced to do. The issue is a lot of the people selling the pitchforks on that side are doing it because it benefits them. That desire to understand encompasses the motives of individual Conservatives and splits them apart. A lot of the issues Conservatives have is that the left is "preachy" that we act like we're better than them and that does come from somewhere. Some leftists do just want to be the smartest most correct person in the room but others are just waiting for the Conservatives they know to be more understanding of other people who they learned about so they stop being mean. The person who pitties the school bully is often their target because that empathy seems to the bully like condescension.