Certainly he was picking holes in Claire but there's one huge difference, he was telling the truth (he found her irritating) and she was lying (she denied kissing Adam). The bit I'm referring to is episode 8 at about 5.30mins in. Jessie goes to talk it out but she is utterly defiant and deflects, preventing Jessie from talking. She keeps demanding an apology for his 'disgusting behavior' so that she sidles out of admitting to hers.
I guess I identify with Jessie as I've been in a relationship with a deceitful gas-lighter and I recognise how it grinds you down and makes you afraid to stand up for yourself. I think Jessie became very keen on her but had enough insight to know that staying with her would have left him vulnerable to future incidences of her lying and denying. Better to cut loose and try to find someone honest.