Its not that they don't have pitch, per se, it's that the nature of the sound they produce makes the concept of "pitch" kind of meaningless.

Except for a pure sine wave, every tone is going to have multiple harmonics over the fundamental which is what actually gives an instrument, even the human voice, its timbre.

Percussion instruments like cymbals and the snare drum create broad-spectrum noise. There's essentially so many frequencies that it's difficult for our brains to nail it down the fundamental pitch. It's also what helps us hear them over the rest of the ensemble.

Drums in general produce very short pulses of sound, which also makes it harder for the brain to tell what pitch it is. In harmonic analysis, any very short sound is actually broad-spectrum because it takes a ton of harmonics to produce a single sharp spike with rapid decay.

I highly recommend downloading a spectrum analyzer app on your phone to get an intuition for this. If you're on Android, I recommend Spectroid.

Just run it and watch the screen while you make different sounds, approach various sound sources, play music, or just talk or sing. If you can whistle, that also produces an interesting result. You can actually see the frequency of the power grid in the harmonics produced by electric motors and transformer coils which is personally really fucking cool.