The verse doesn't say that God asked Adam to teach them the names, the verse says that God asked Adam to inform them about the names. The verb used is «نبء» not «علم». Their usage is quite different is Quran.
The following is what I understand from Quran:
The reason God tells Adam to inform the Angels about the names seems to be that God wants to demonstrate to them that the creation of Adam is justified. If you look at the verses about the story, you see that the Angels are objecting to the creation of Adam and say that they already do worship God so why create Adam and put him as Caliph on Earth? By teaching the names to Adam and asking him to inform the Angels about the names God demonstrate to the Angels that Adam is capable of worshiping God in a way that the Angels are not capable of, that is Adam is capable of learning the names while the Angels are not capable of learning the names.