First off, I think the divide between sciences and humanities is at least somewhat dodgy.
That said, I think a lot of claims about the necessity of humanities for critical thinking are dodgy too. You know what forces learning critical thinking, since it absolutely is ruthless about cherished assumptions? Debugging. You may hold whatever beliefs you like about the behaviour of a piece of code, but if they don't correspond with reality, you will crash against a debugger until you correct them. And, most often if you're debugging in the first place, it's because you thought something wrong about the code to begin with. Debugging is a systematic and merciless machine for changing one's mind. If you can't change your mind, you can't debug.
Also, the notion that humanities somehow exempts or protects against the ethical drift that many people in technical fields fall into is ludicrous. It's capitalism and profits, not maths, causing the damage. Kissinger studied political science and history, not physics.
Redrafted because, as usual, I made typos.
