It's not fully just a tic of language, though. Responses that start off with "You're right!" are alignment mechanisms. The LLM, with its single-token prediction approach, follows up with a suggestion that much more closely follows the user's desires, instead of latching onto it's own previous approach.
The other tic I love is "Actually, that's not right." That happens because once agents finish their tool-calling, they'll do a self-reflection step. That generates the "here's what I did response" or, if it sees an error, the "Actually, ..." change in approach. And again, that message contains a stub of how the approach should change, which allows the subsequent tool calls to actually pull that thread instead of stubbornly sticking to its guns.
The people behind the agents are fighting with the LLM just as much as we are, I'm pretty sure!