Frankly, though, I'd prefer no one ever used the "conventional language of probability", because it leads to precisely these miscommunications. If the question

Frankly, though, I'd prefer no one ever used the "conventional language of probability", because it leads to precisely these miscommunications. If the question had been phrased "Out of two-children families that have at least one boy born on Tuesday, what proportion have a girl? [on natural assumptions about lack of biases or correlations concerning the distribution of children's genders and days]", would you agree that the answer was 14/27? That was the question the author intended to ask. The dispute may simply be as to whether the question which the author did ask is equivalent to the above; if that is indeed our only disagreement, we can still investigate that dispute further, if you like. But let's first see if the dispute is linguistic or mathematical.