Men also prefer tall men - the taller candidate nearly always wins the presidency and taller guys have been shown to get hired more often and to earn more when they do. This is a function of patriarchy, because it's a dominance-based hierarchy, where being tall might well provide the advantage of being seen as more powerful. As for women wanting someone to protect them from other men, this only really became "a thing" since the advent of patriarchy about 6-9k years ago as well. Prior to that time, a tribe or community looked out for and protected everyone within it as a primary survival strategy.

We're all steeped in patriarchy our entire lives so it's not surprising that you may have absorbed some of that.