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You say this when someone is trying to flirt with you but you think they're the worst. Like a gay guy hitting on a straight guy who's just there for the snacks.
'I don't go that way' after the guy in the coffee shop asked me if I wanted to go to the movies. I just wanted my latte.
'I don't go that way' when my cousin hit on my dad at the family reunion. Dad was confused, I was laughing.
'I don't go that way' when my friend's crush came on to me at the party. I was just there for the pizza.