Why did Sinon act strangely when Kirito grabbed her tail? I noticed in an episode of Sword Art Online II (Calibur arc) that Sinon (a Cait Sith) reacted strangely when Kirito grabbed her tail. Silica (also a Cath Sith) noticed this but it seems that she too (just like me) has no idea. What happened here?
The following is quoted from Sword Art Online Book 8: Early and Late, page 221


  The triangular ears and tail unique to the Cait Sith race were of
  course organs human don’t have, however, they could sense the feeling
  using an unknown mechanism. Being grabbed hard by a player who
  wasn’t aware of the fact would cause a «super weird feeling»——
  Silica’s explanation——for that reason, the reaction was always very
  amusing.


This quote actually shows us a few things:


Why Kirito pulled her tail in the first place: it's "amusing"
What it feels like: "a super weird feeling" cause by sensentations from an organ humans don't normally have - similar to the wings in ALO, I might add
Why Silica looks at her tail in the YouTube clip: calling it a "super weird feeling" was her description, so she clearly knows how it feels. In other words, it's likely that someone (possibly Kirito, since he seems to enjoy it so much) has done the same thing to her.


I've added the picture of this scene from the light novel just for reference.