A phrase one uses when they don't want to or don't like doing a certain thing.
Mel: Damn check out
Rick's nice ass
Bob: Uhh no thanks, I don't swing that way
Mel: You did last year with Mike
Bob: Shh, only that once...
Kevin: Hey Tom, We're going to tax shit from Wal-Mart, wanna come?
Tom: Sorry dude, i don't swing that way.
Tom: Mm Pussy, i DO swing THAT way.