Anyone else who understands sarcasm, but gets bothered with logical inconsistencies?

Anyone else here with similar experiences?

So, I like to think that I can perfectly identify when someone is being sarcastic. BUT, I get super bothered with logical inconsistencies within their sarcasm.

Friend: "Premise X (mostly unsaid, assumed to be common shared knowledge/experience), inference Y (to be assumed by listener), conclusion Z (stated as the opposite of the conclusion because sarcasm)".

Most of the time, X is false/more untrue than true, and Y doesn't make sense.

I: "I understand that you're being sarcastic, but your sarcasm doesn't make sense."

Friend: "It's not that deep bro"

I: "But it still doesn't make sense. Words have meanings, and what you said... Doesn't make sense"

Friend: Gets annoyed/chuckles to themself.

SO. Anyone else here who experiences this phenomenon? It's bloody annoying, and makes conversations frustrating. You either have to shut up and let them continue talking nonsense (which is torture), or interject, thus making a fool out of yourself.