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I think "I don't believe this is sincere" is in response to him saying he believes it's for the best for both of them.

Astarion: There's no use in us fighting any longer, is there? You are a person of rare talent. You aided greatly in my conquest, even if you did not end up a part of it. And if we were beholden to one another? Well, how is that too different to being enslaved? It is for the best.

Player: I don't believe this is sincere.

I've always seen that quote as evidence that Astarion is trying to convince primarily himself that “it's for the best”. And Tav doesn't believe that Astarion actually believes that. Likewise, I take the rest of the dialog the same way. As a way to cope with the breakup and devalue the relationship itself. There's nothing but bitterness in his words.