I expect it goes back to bullying, dominating another person, and the feelings of anger, shame or humiliation or simple lack of control that someone else made us feel in a /very/ different context growing up. If you /say/ "tickle," someone might tickle you. If someone else says tickle it opens the possibility that someone might try to tickle you.
I was backstage at a production of some community theater thing and there was an older guy who liked to play around and tickle younger actresses (usually legal) and he would sometimes do this for extended sessions. I'd have to pretend to just be amused and then, after awhile, help the poor girls (who generally weren't fighting /that/ hard) by saying "OK, I'm not sure what's going on here, but I'm pretty sure you won." He once said "Hey, who's ticklish?" and started tickling all of us. I was really worried that I'd be identified as a ticklefreak, but he only tickled me for half a second and I didn't even laugh.
So even when it comes up in a public context, you can bluff your way through. Unless, you know, you /want/ everyone at the booth table you're trapped in to all start tickling you, in which case ... bring it up yourself! 😀