If you are liberal, you think people should live to be happy ; you think that a good community, a good company, or a good family helps its members to flourish.
If you're a liberal you think people have a right to free speech and that no religion should be favored over any other (even over no religion) in public affairs. If you're a liberal you think a person has the right to choose how to use his own body, and since again, you are against sexism, that means a woman has a right to choose whether to bear children and whether to have an abortion . You're in favor of access to birth control and support sexual freedom and gay marriage .
These are all reasons to appreciate the life philosophy and politics of Objectivism. They are reasons to like Ayn Rand. (And as Michael Shermer pointed out last year , if you're liberal, you should find a lot to love in Atlas Shrugged, starting with Rand's depiction of the heroine, Dagny Taggart .)
If you're liberal, you may confuse favoring something with thinking it should be subsidized. You may confuse crony capitalism with free markets and confuse the president with Santa Claus. And liberals are tempted sometimes to reject logic in the name of muliculturalism and toleration, but Ayn Rand will set you straight on those issues, for sure. Because if you are liberal, you still believe that reason is how we know the truth and you defend science. Rand called her philosophy Objectivism to put the focus on just this issue.