Why Would Conservatives Change when Liberals Don't?

In the debates around "merit", the conservatives have a very straightforward view - "hierarchy is natural, one should only care about oneself and getting ahead in one's life". The liberals, on the other hand, are the confused bunch. They have a hatred for hierarchy, but they live and breathe hierarchy too. They hate that people get ahead of others without caring for others, but they are compelled to do the same too.

And conservatives are quick to spot this. They will ask the liberal who talks about equity - "Why do you hold on to your privileges and ask others to give up theirs?"

I think they have a point. Why do liberals hold on to their privileges and ask others to give up theirs?

In x + y, Eugenia Cheng talks about how the world is set up for competition. That the world rewards those who do not care about others and in turn those who don't care for others "succeed". And Eugenia Cheng also urges us to look for solutions all around us, to try and convert competitions into collaborations.

But how many liberals are actually able to do that?

Aren't liberals using their accumulated privileges to accumulate more privileges?

Aren't liberals continuing in power hierarchies without destroying the hierarchy?

Aren't liberals legitimizing the very structures they hold responsible for the problems?

Aren't liberals trying to get ahead of others? Aren't they competing? Aren't they reinforcing the very notions of merit that they oppose?

If liberals don't change how they live their life, why would conservatives do?