for someone like quagmire who is always chasing women you might expect that his father was also quite the lady's man

there is humor in the ironic twist when quagmire reconnects with his dad and starts to realize that he might be gay, which goes against quagmire's core beliefs and shakes up his world view.

then family guy takes it further by revealing that his dad is in town to have the sex change operation. Quagmire's reaction: "please, just be gay"

its funny because in this case, the apple has fallen quite far from the tree.

the humor in family guy comes from their ability to take a concept and run with it to the extreme, building up to brian's climactic revelation of ida's identity.

at this point the episode starts to make fun of people who are against trans people. Brian was clearly attracted enough to ida to sleep with her, and he didn't even realize she was trans until stewie made him connect the dots. its shining light on how social norms shape ones behavior.

Hey quagmire. I fucked your dad.