I don't think you do understand the problem. The thing you're taking issue with - GB vs BG - is the vitally important to the statistics, and is the thing that "normal" people get wrong when they see this kind of problem for the first time.

The only real objection to the problem as it's posed is that it's pretty unlikely that anyone would say that one of their children was a girl when both of their children are girls. For a normal conversation, the ambiguity wouldn't be present; "two children" combined with "one is a girl" means the chances of one boy and one girl are 100%.

It's a bit like the old joke about "which month of the year has 28 days?" - answer being, they all have 28 days, just some have more.

However, in other less contrived situations, this is important. People risk discounting permutations, and only considering combinations, when the permutations are necessary to get a correct view of the odds.