Context is everything. The reason it made you uncomfortable to hear this from your neighbor is that he's male, you didn't ask him, and a discussion of sex was inappropriate. This wasn't a discussion of sex, exactly--he probably felt like it was OK to talk about this stuff because he was talking about sexual education rather than sex. I think he was wrong, since you were uncomfortable (and probably squirming) and hadn't said, "Tell me all about your philosophy of openness about teaching about the human body, please. Spare nothing, for I have all day. In fact, get the charts."
I don't think the words we use are sufficient if we don't know the parts of our own bodies. Men complain that women's bodies are mysterious, and women themselves often do not know where the clitoris is. That's kind of major! (Since our context is a discussion of whether to talk about parts by name, I think politeness permits me. You may shield your eyes if you so choose.)
In essence, I think your neighbor was right that people need to know this stuff. By the same token, it's valuable to know the names and purposes of our internal organs, but it's not polite to stand around discussing how our pancreas and Islets of Langerhans, or even bowels or lungs, are functioning with a neighbor who hasn't asked. It's true that genital organs include both internal and external parts, but we as a society learn not to discuss them in detail while standing on street corners, unless we are flouting rules of politeness.
I get the idea of using "correct" terminology, but I just don't like how it feels. Like one time, I was talking to a neighbor; his wife was out of town for a couple days, and I didn't remember exactly why, so I asked, right? Big mistake. He told me she was at a workshop to teach people how to teach sex ed to adolescents at UU church. He proceeded to go on a tangent about how people needed to know and use the right word for the right thing and then went on to use every single word and description in graphic detail. ICKY. It really disgusted me that this guy would go out of his way to make a point about "correct terminology", like it was so PC, when in fact it was just gross. I never spoke to him alone after that. And it just cemented my stance that the words we use are perfectly sufficient. lol