Technically the reason tweeters are the parts killed when an amplifier is pushed beyond it's capability is the clipping waveform (if you could see it on an oscilloscope) the top and bottom of the waves in the waveform get cut straight across as the wave exceeds the range it can be amplified properly. So those cut off parts are squared off 'hard' in most solid state amps. The 'square' corners are actually a higher frequency part, that should not be like that. (tube amps tend to 'clip with rounded 'square' clipping, so they are gentler on the speakers tweeters, and have what is called 'soft clipping'.)
The tweeters usually carry only a tiny part of the total signal, and are safely designed to only carry a few (up to a few dozen) watts of power, even in really powerful speakers, So those cut off waveforms suddenly are sending really a LOT of wattage in high frequency content to the speakers, and your tweeters overheat fast, and die.
Even only a few minutes of clipping hard with an underpowered solid state amp can fry the tweeters.
An amplifier with way more power than the speaker can handle, will not burn out the tweeters. It may blow up the speakers, (along with your hearing) but not just the tweeters.) and if it is really super loud for only a short time, the speakers can survive (because the entire speaker parts, all coils, and crossover parts are equally being stressed/heated). so too much power is ALWAYS better than clipping.
