Not responding to the US drone being shot down while in International waters wouldve been a sign of weakness. He had to answer back somehow, perhaps he initially never wanted to attack Iran, prompting the military to attack isn't the most diplomatic of approaches but it does send some kind of message that says that the US military isn't afraid and won't back down
He didn't respond though lmao, and the US military did back down lmao, WHAT ARE YOU TALKING ABOUT
also there is other ways to respond to that than authorizing strikes, you can't make these decisions without thinking about the consequences, and also backing down shows the US can be back down