Consider the Tory election poster of 1987 with the legend: Labour say he's Black, we say he's British. The second clause is supposed to contrast the first. More precisely, the sentence implies that the property P2 attributed by the second clause excludes the property P1 attributed by the first clause, at least for the subject of the sentence, at the time of utterance. The sense of exclude I have in mind here is something like: if P1 and P2 exclude each other, then P1 and P2 are not jointly true.
An example: John says it's margarine, Peter says it's butter. I think Peter clearly means to rule out the possibility that John is now spreading margarine on his toast.
A possible objection is that this implication will only work for some P1 and P2 that can't be coinstantiated anyway. I don't think so. Consider the example: Ali says it's sweet, Sophie says it's sour. Even in this case, where the pork could be both sweet and sour, the clear implication is that the pork is either sweet or sour, and it's not both sweet and sour.
I think the implication is true of most (or all) sentences of the same form.