Not weird at all. In fact, this happens all the time. You should keep your eyes open!

I'll bet you didn't even notice when President Obama fired Michael Flynn, Director of the Defense Intelligence Agency, for being "abusive with staff, didn't listen, worked against policy, bad management, etc.". Against Obama's recommendation, Flynn was later appointed by President Trump to be National Security Advisor  and then fired 24 days later for an extremely interesting variety of misbehaviors.

Stephen J. Remington