The Left often claims to be in the "right side of history" because there is a certain pattern for this claim:
A society is formed and goes well, but certain people are left behind: a group then fights to make changes so this group is guaranteed to have all the rights and duties a citizen should have.
There have been cases where the left did this and it worked, so they've claimed "they're the good guys of history, bringing change and revolution". Alas, they ignore that people who aren't leftists have also made different changes as well.
The problem with this group is that they aren't always driven by morals. For example, the conquest of t he Americas: when the Spaniards arrived to America, the whole world changed. There were bad consequences, but also very good consequences such as cultural diversity (the good one), more trade, discoveries, technology, and so on. They didn't do it because "it was the right thing to do!" but because "fuck it, let's do it!".
The Left, on the contrary, is driven by "it's the right thing to do" and they go for the sure safe thing, like Civil Rights. Giving black people full rights is a good thing, not saying it's not, but they aren't actually risking much historically speaking. The goal was to give a group of people fully acknowledged rights, and the sacrifices made were worth it. But, with the previous example, the conquest of America, the final goal wasn't as "noble" so the bad consequences of it are seen as an "well, I told you so!". That's why they still try to get away with the "we're in the right side of history" nonsese despite the left has been responsible for very high death tolls such as Communism or the French Revolution: they were only trying to improve the world!!!
