It's wrong to trick people into thinking you can sing.
Jess would brag that she could do anything, so when one of her friend brought up singing she said she could do that too.
Jess wants to end the discussion.
Jess points out that technically anyone can sing, using auto-tune.
Jess insists that she can sing better than any of them could.
Her friends all laugh and admit it's technically true and move on to the next thing.
Of course no one believes Jess, and when she brags the next time no one believes her then either.