Easy - I don't think that, so it's not justified. The opinions of "the vast majority of humanity" are not part of the decision making process that has resulted in this situation.
> I wonder if it's possible to describe this as a series of logical axioms
I don't wonder, I believe it is! These are the (simplified) axioms along which I form my opinions about not only this, but all geopolitics in general:
- Actions that cause human suffering are bad.
- Actions that reduce human suffering are good.
- Innocent suffering in a conflict is inevitable.
- Force will be required; conflict is inevitable; the world is imperfect.
- The use of force is righteous or not depending on how the resultant innocent suffering is accounted for before, during, and after.
I believe that my opinion is completely consistent with these statements. You asked if using violence to stop other violence is wrong, and my answer is "it depends". If the Houthis were taking action against the those actually committing the atrocities, we'd probably not be having this conversation. Deliberately causing harm to innocents is never acceptable, never right. This is terrorism as a tactic.
If you think that second order violence IS an acceptable course of action, where do you draw the line? How much societal disruption in countries with less food security are we willing to induce?