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Because it's common courtesy to shut-up and stand at attention while the anthem of your host nation is playing. It's called respect, something that was lacking on this ocassion.
Respect goes both ways, of course: it's also "common courtesy" not to start playing loud music in the middle of a sentence being delivered to a state event by a head of state. Seems to me everybody involved was trying, in good faith, to be respectful and follow protocol, and things got deeply confused and entered territory with improbably conflicting protocols. By default, cultural instincts would then guide on-the-spot reactions to the conflict. Unsurprisingly, people attuned to different cultures would have different on-the-spot reactions.
The band did not just start playing at random... They received their que. Most people give the same simple toast, "To the Queen!" When the band hears this, they play. The President was ignorant enough of protocol to put those words into the middle of his speech. He was wrong. Period, plain and simple. However... this is not truly the President's fault. It's the fault of his handlers.