Our experience with learning about the world should teach us that our intuitions, while useful, cannot be fully trusted. It intuitively feels wrong when we learn the Earth is rotating. It intuitively felt wrong to me as a kid to learn that two objects will fall at the same speed regardless of their weight. It's not initially intuitive that heavy boats can float, or planes can fly, or that these yellow lines are the same length, or that eating a pill can cure a headache. The Monty Hall problem still confuses me. Etc.
And yet we seem unwilling to accept that our intuitions can be wrong about morality. An extremely common rebuttal to any moral philosophy is to come up with a hypothetical scenario where that system of ethics would lead to a conclusion that strikes us as intuitively wrong. But so what? Even just the fact that different people have different moral intuitions should make it clear that we should expect our intuitions to be wrong in some cases.
A couple of examples:
The second half of the trolley problem is often used as a rebuttal to consequentialism. Yes, it feels intuitively wrong to push the guy in that scenario. But especially for very unrealistic thought experiments like that, we shouldn't find it impossible to believe our intuition could be wrong in that case.
The Euthyphro dilemma. I was listening to the Rationally Speaking podcast and was confused to hear the host say that the idea that morality can come from a deity is refuted by this dilemma because that would mean "might makes right". Huh? If it is true that morality is the will of a deity, then it is true that "might makes right" in that case, even though those words thrown together produce a negative intuitive reaction.
I do think pointing out unintuitive cases of anyone's moral reasoning (especially your own!) can be interesting and fun. And it's a good way to challenge whether or not you, or someone, really believes what they think they believe. But it doesn't mean the ethical system in question must be wrong.