I tried to join a boxing gym, but they told me I wasn't cut out for it.

This joke lands its punch through clever wordplay, specifically a pun on the common idiom "cut out for it." When someone says you're "not cut out for" something, they mean you lack the natural talent or temperament for that activity. The setup leads us to believe the speaker simply isn't suited for boxing.

However, the punchline delivers a literal, physical interpretation. "Air punches" are exactly what they sound like: punches thrown without making contact with a target. While shadow boxing involves throwing air punches as a training exercise, in a real boxing scenario, consistently throwing air punches means you're missing your opponent entirely. The humor comes from the sudden shift from a metaphorical lack of suitability to a very literal, and quite embarrassing, inability to connect.

It highlights the fundamental skill of boxing – actually hitting something – and contrasts it with the comedic image of someone flailing wildly without making any impact. The joke playfully suggests that the aspiring boxer's lack of aptitude is so profound, they can't even manage to hit the air, let alone an opponent or a punching bag.