It's kind of hard to have a romance with someone when you can't touch them, but that's the reality — or fantasy (because who knows what's real at this point) — that Syd and David are dealing with on Legion. As the second episode had them both living in the seemingly friendly facility of Summerland, they've had a second chance to connect after their disastrous time at Clockworks Psychiatric Hospital. Yet, Syd and David still can't touch on Legion, despite the change of location. That's because although David is perhaps the most powerful mutant, Syd's inability to touch people comes from her own powers.
As Syd Barrett is not from the X-Men comics (and yes, she intentionally shares her name with the founding member of Pink Floyd), viewers of the FX series don't have a lot to work with when it comes to understanding her character — and her powers — just yet. However, what has been revealed in the first two episodes is that when she is touched, she trades bodies with the person who touched her. So far in Legion, this phenomenon has only happened between her and David Haller, but it has been implied that it's not specific to Syd and David. As showrunner Noah Hawley explained to Entertainment Weekly:
Rachel Keller, who portrays David's love interest Syd, also confirmed this in an interview with Vulture when she said, "... my ability involves touch and not being able to touch anyone." Even casual X-Men fans will recognize that comic and movie character Rogue has similar powers to Syd and that beyond being a liability, they can be an asset.
However, what makes it catastrophic when she touches David is his own incredible powers. When they traded bodies in Episode 1, she unintentionally killed David's friend Lenny due to not being able to handle David's power-ridden mind and body. As Lenny said, "Don't give a newbie a bazooka and act surprised when she blows sh*t up."
Presumably because of her power to transition bodies, it also is uncomfortable for Syd to touch anyone else. She does wear gloves to help stop skin-to-skin contact, but when David wanted to hold hands with her since it seemed like the only viable option for touching, she told him it's not pleasant for her. And why should it be? If you've spent your entire life having to avoid being touched, holding hands through fabric doesn't sound that appealing.
Yet, what's interesting to note is that Syd told David that they could hold hands at the end of Episode 2 if it would stop him from leaving Summerland. It seemed like part self-consciousness and guilt over the fact that she thinks he wants to be able to touch her and part desperate act to keep him there. While she shouldn't feel bad about her amazing ability, it wouldn't hurt if Melanie Bird taught Syd how to control it. That way her body wouldn't immediately swap with someone else's upon immediate contact and she could better wield her power.
Of course, all of this theorizing about Syd in Legion will be for naught if she's a figment of David's mind. And I certainly won't feel too bad for her if Bird turns out to be evil and Syd has been conspiring with her to keep David at Summerland. But if you take what has been presented to us as fact, then Syd and David will continue having to avoid skin contact until she learns to harness this ability — and when she does, she'll be a pretty powerful mutant in her own right.