I understand both Rhaenyra and Corlys.

Sorry for my bad English. It's not my first language.

Rhaenyra - Rhaenyra was thinking of Joffrey. A lot of you are forgetting she's a grieving mother who lost 2 sons to this war. Legitimizing bastards immediately after ascending the throne would not be a good look for her and would cast an even bigger shadow on the poor boy. "Rumors" about her sons parentage plagued them since the very beginning. So I understand her reluctance, especially now that all eyes are on her.

She didn't even flat out say no, she just said "not now" and wait until all things are settled (or at least that's how I got out of their conversation). Rhaenyra has already been established to be the type of person to keep her word. She freed Mysaria in S2 (Daemon's promise but she considered it as a promise to her house/crown) and even remembered her promise to Hugh. IIRC she started her conversation with Hugh with something along the lines of "Ah, yes, so about what I promised you... I don't understand why a lot of you are convinced that it's a farfetched idea that Rhaenyra would keep her word. Also, how are we forgetting that Corlys is also partially responsible for Rhaenyra having bastards. He knew Laenor was gay, but pushed for the marriage anyway.

Corlys - I, too, would be pissed if I lost my wife, children, (illegitimate) and treasures, for someone who can't even grant me a simple act. He has every right to demand it immediately. He probably took it like how you would react when you asked your boss a raise/promotion and they said not now. Which would probably mean never.

He is also very old and could die at any moment. This man has been obsessed with legacy his entire life. Corlys got pissed because his legacy is unclear when at his age he should've had an uncontested heir by now. He had decades to legitimize them but only came to care about them now and was trying to redeem himself for the years he spent turning a blind eye by legitimizing them and making their lives better. Him being pushy and frantic about it is justified.