引く here is colloquial slang — 'to be put off, weirded out, to recoil' (from the literal 'to pull back, withdraw'). 逆に is the discourse adverb 'on the contrary, conversely,' marking a counter-intuitive observation. ~ちゃう is the colloquial contraction of ~てしまう. The と after 美人だ is a general-condition conditional ('when/if X is the case'). でしょう as a stand-alone response means 'right? I know, right?' — an agreement-seeking return.