Fears and phobias make great character flaws for roleplaying. Remember that there's a technical difference. A fear is something that you worry about or don't like, while a phobia is a psychological reaction that is very difficult to control.
So a fear can be roleplayed by the player, and the character can potentially steel themselves mentally and overcome it. But a phobia is more difficult. If you take a phobia-level flaw, it's potentially justifiable for the GM to forbid certain actions. For example, if your PC had full-blown Arachnophobia, it would arguably be justified for the GM to completely forbid you from wilfully approaching any spiders. At the very least, any attempt to overcome the phobia, perhaps with a Will roll or something, should be very difficult.
Commentary by memnarch (who has not seen the movie)
A little rude of the GM to not allow contact to be broken in this case. Rey wasn't attempting to read Ren's mind, just resist against the mind reading; the critical success just seems like it would give the bonus effect. I would have given Rey the same info, but then have had Pete and Sally do another opposed roll for breaking the link. In that case, Rey would be trying to maintain the new link while Kylo tries blocking her out from even more info.
As weak as Darth Vader? That is very specific. And I think, a rather inaccurate assessment as well. To paraphrase, she commanded the Galactic Empire and couldn't die until she wanted to. It also doesn't feel like that would fit with Kylo's insistence of holding onto the helmet. And the whole Vader groupie look? There's no reason to go with that outfit if Kylo thinks Vader was a weakling, unless Kylo is trying to redeem the look for some reason.
Hm, if Pete is again surprised by what Sally chose for her character, is she getting to be just as big a munchkin as Pete?
Transcript
GM: Here, Pete, you learn this from Kylo’s mind.
Rey: You... you’re afraid...
Kylo Ren: I break off contact!
GM: You can’t.
Rey: Afraid that you will be...
Kylo Ren: Stop!
Rey: ... as weak as...
Kylo Ren: Argh!
Rey: Darth Vader!
Kylo Ren: Noooooo!
Rey: That’s a very oddly specific thing to be afraid of.
Kylo Ren: I considered Arachnophobia, but needed something narrower to stay within the Flaw limit.