There are many reasons that someone could want to make fun of an STD, but I feel like the most common reason is if someone feels uncomfortable about it. People make jokes about sex, racism, death, and various other topics that are "sensitive". Humor is one way to cope with an idea in a light hearted way, and if someone doesn't feel comfortable with such a serious topic like STDs, then humor may be the only way they can discuss it. I highly doubt that the jokes are ever meant to be insulting, even though sometimes they can come off that way (many jokes about toughy topics can come off in a bad light, especailly if someone takes that topic close-to-home).
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So when you're happy (Hurray!), or sad (Aw!),
Or frightened (Eeek!), or mad (Rats!)
An interjection starts a sentence right.