Do women actually care about height?

A lot of dudes seem fixated on height if they are short and think it's a deal breaker or it makes it impossible to get women. One friend in particular railed against females putting in "minimum height" in dating websites. I tried to point out that he still has more success despite him being 4"7' and me being 5"8'. What is so attractive about it that justifies the obsession with it? The grass is always greener. If you're tall you just find something else to be insecure about. That's human nature