I remember “mailman” and “policeman”. I remember objecting to the terms, and making the same stupid comment: “So what, is it going to be a personhole cover next?”
Which just goes to show how big of an idiot I was back in the late 80’s.
I’ve since learned better – but it can be really hard sometimes to explain to others why we should make certain word choices and not others. Here, let’s have a re-enactment:
Random Person: “Don’t do a half-assed job of that.”
Me: “Y’know, half-assed is a sexist phrase.”
Me: “Yeah. It refers to the way women had to ride sidesaddle. So it means doing it like a woman.” 
RP: “So what if half-assed used to be sexist? I don’t use it that way.”
The Portly Dyke helps. In “Watch Your Mouth” (part one, part two, and part three) she clearly runs through how to determine when it’s a bad idea to use such terms (and why), how these sorts of words get changed, reappropriated, and co-opted, and what you should do instead.
These should be required reading. Get to it. 🙂
 Yes, I know that you can find places online that claim the term “half-assed” comes from other, non-sexist roots. Except… well, none of them agree on the origin of the phrase, which means that I’m far from convinced of their explanations. I mean, this idea of “half-adzed” sounds like a post-facto justification, which disagrees with all of the possible origins at dictionary.com – and those disagree among themselves on the etymology and the date of origin Let’s just go with the example, okay?