When speaking with authority makes you feel arrogant

In the meeting I knew the answer cold — I've done this a hundred times. But the second I said it plainly, with any weight behind it, a voice in my head hissed that I was being arrogant, full of myself, too much. So I hedged and softened until my own certainty sounded like a maybe. I know what I'm talking about, and I still can't let myself sound like it.