Honestly, I think Iino interaction with Ishigami is because how those two always are.
I'll take myself for example, but I'm absolutely terrible at dealing with depressed people. The best I can do is cracking some poor jokes, staying friendly and trying to banter a bit to cheer them up back to their usual self.
I think that's what Iino tried to do. She wanted to make him react with their usual banter when she goes overboard and he tsukkomi her. Simply because SHE DOESN'T KNOW what else to answer.
But that backfired horribly here because she trashtalked and made him feel even worse.