I intuitively feel that there really are objective morals (or: objective mathematics, actual free will, tables and chairs, minds).

Therefore, there really are objective morals (etc.).

"Morals" is just a word. But unlike some other words, it's not 100% clear to me what it means. There is no physical entity that "morals" clearly refers to. There is no agreed upon list of axioms that define what "morals" is. That's why, to me, "there are objective morals" doesn't feel entirely like a factual statement.

I might justify that there are objective morals by relying on my intuition. But that's not because I think intuitions are reliable sources of knowledge. That's because I think intuitions are the correct normative source of how we use words (together with common usage, I guess).

It's till possible that my intuitions contradict each other, or that they contradict facts. So they are not sufficient to say with confidence that objective morals exist. But they are relevant.