Well, I think by definition, "normal" implies "good" and "right." Clearly that isn't always the case since context is everything (not to mention subjective), but since "abnormal" is in general used to imply that there's something wrong with someone/something, I think "normal" implies "acceptable/correct/best."

So while I'm sure Buffy didn't mean to hurt him, and I don't know if she aspires to be normal or what her context is, I think that yes, the statement "you're not normal" is inherently offensive.