The liberal left is neither a singular entity nor even a single group or organization.
Liberalism is a mindset just as conservatism is a mindset.
I am sure that most individuals afflicted with a liberal mindset would be unable to name any particular goal for their beliefs. Most often these attitudes and opinions are not of their own formation or arrived at through considered thought. Instead, they are learned from others' repeated pronouncements of them. Those making these statements often have come to learn them in the same way. Much the same as fables and Bible stories are passed down from generation to generation.