I agree with you 100%, SOH.
penis and vulva are not 'medical' terms, in the way that 'mandible' is.
It really is all to do with some unconscious feeling that anything to do with the genitals is wrong, dirty, naughty, rude... and rather than see that's all it is, we seek to find justifications for saying winky or foofy, because it's wrong to say penis and vulva, it's naughty. It's dirty. They are words that children don't need to know!
I blame the Victorians 
When you think about it - if you say foofy, you mean vulva or whathaveyou, you know you mean it, you know that's the body part you're on about, so the problem is simply the name.
I don't get it.
It's like that whole spider / loofah thing on here ages ago 
Call a spider a loofah if it makes you feel better, but it's still a spider and when you say loofah you're still thinking/seeing/saying spider. So you're just avoiding a word. A collection of letters.
That is so illogical that it can only be an irrational fear or disgust.