Freaky, except they're only a few millimetres in size and considered harmless to humans.

It would be hard for a spider of medically significant size to suck down their exoskeleton like that.

Lots of fears are visceral, but even if we were to allow only verbalizable fears, one could imagine the arachnophobes thinking "what if this tiny spider burrows through my eyes or ears and lays eggs inside my brain, and then all the baby spiders stream out of my mouth and nostrils"

Why? You could probably wear those much like you would a ring or a bracelet.

I do believe there also is a song about them. It goes something like this: Anywhere you go, you always take your spider, your spider with you... ;)