Why did the harmonica feel left out?

This joke strikes a chord with its clever use of wordplay, a classic humor mechanism that relies on a single phrase having multiple meanings. In this case, the phrase "blown off" is the star. When we talk about people, "being blown off" means to be ignored, dismissed, or stood up, which is a feeling no one, not even a musical instrument, enjoys.

However, for a harmonica, "blown off" takes on a literal and essential meaning. Harmonicas are wind instruments, and to play them, you quite literally have to "blow" into and "draw" air out of them. So, while the setup suggests the harmonica feels neglected, the punchline playfully reinterprets that neglect as the very act of its existence and how it's played. It's a silly twist that makes us chuckle at the double entendre.