It's a simple case of "they started it". The Houthis are the ones who resorted to violence, against innocent civilians who had nothing to do with the conflict in any way.

Just because we have so far successfully shot down their missiles doesn't change the intent behind the attacks, to kill civilians and cripple international shipping.

You don't negotiate with a madman shooting wildly into a crowd, you take him down. And they did so in the most humane way they could, targeting only missile sites, basically they are trying to take the gun away from a violent idiot.