Millions of liberal men can man just fine every day just out in public.

That is true, absolutely. And one must not diminish the situation of women under the patriarchy by any means.

Unfortunately, the patriarchy damages all of us in different ways. That does not contradict feminism but, in my estimation, completes the view of the patriarchy, it's effects, and how we perpetuate it generation after generation. I think if we wish to be anti-sexist and pro-feminist and ever hope to abolish the patriarchy, we must understand it as fully as possible.

If you care to explore the topic further, "The Will to Change" by Bell Hooks might be worth a read.