Gavriel is sent to destroy Jerusalem, Hashem commands him to fill his hands with fiery coals from the hands of the Cherub. Gavriel goes to the Cherub, (understood to be Michael), Explains what he's supposed to do, Michael says, 'take the coals', Gavriel says'put them in my hands', directly disobeying G-d, with consequence. He is cast out from behind the curtain and lashed 60 times, and replaced by Dubiel, the angel of Perisa, for 21 days. (yoma 77a, tanchuma tazria 9, see also Malachei Elyon by Reuven Margoleous).
My friend said in the name of his rabbi that angels are preprogrammed to act in certain ways, regardless of whether or not those ways are right or in accordance with Hashem's will. I asked my rebbi, Rav Aron Lopiansky what angels are, he said that 'they are middos of HKBH that sometimes take on minds of their own'. So they disobey Him sometimes, because that is how they were made to act.
So the angels got upset that Moshe was taking the torah because they were created to act that way at that time, probably to teach us something, as the story is related in the Talmud.