"We cannot talk" is, arguably, a close relative of Moore's 'paradox': "It is raining, but I do not believe it is raining".
There are lots of detailed explications of this very odd statement, but it seems to me that there is a distinction that could help us to understand (and 'solve') it - between self-contradictory statements (e.g. the Liar) and statements which are incoherent with their own status as statements.
"I cannot talk" is clearly an example of the latter. It makes perfect sense to say "X cannot talk" where X is a third party - a mute, an animal or an object; but not where we substitute the author of the statement into X. If you can't talk, you can't say so either; so if you utter these words, you either cannot be saying what they are normally taken to mean (i.e. that potential interpretaion is barred - no charitable principle can rescue it) or you are not meaning to talk seriously - perhaps you are doing a bit of contentless verbalising, or playing word games.
In the traditional formulation, "It's raining" and "I don't believe it's raining" from the same speaker are not directly contradictory, but they do challenge each other's intelligibility. Making both statements is so grossly inconsistent with the context of assertion combined what we normally mean by "believe" that they are rendered unintelligible. An interlocutor who makes these statements, as serious contributions to a conversation, is either revealing an inability to converse or seeking to undermine the game.
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