I have no idea why an FA would expect to "overrule" the captain. That is bizare.
There is no way to know exactly what the core issue was. It wsa not because the air was off for a few minutes as that is common.
If, for example, the reason was that the elextronics were screwy and he did not feal it safe, would it have been in the best interest of the passengers and DL to fly simply because the aircon came back on?