The correct answer has nothing to do with the number of families. This is a very tricky problem, and many people fall into the trap of trying to average each possible fraction of girls, weighted only by the probability of that outcome. But in fact they would need to be weighted also by the size of the population, if that strategy is used to find the answer.
Google's reasoning is perfectly correct, but here is another route to the same result. We just find the expected number of boys and the expected number of girls for one family.
The number of boys is obviously 1 for any outcome (of the form GnB), and so its expectation is 1.
The expected number of girls is given by the summation of n·p(n) for n = 0 to ∞, where p(n) = the probability of the outcome GnB, which is 1/2n+1. This sum is perhaps surprisingly also 1, which is easy to verify.
Thus each family's expected number of children is 1+1 = 2, and for N families, this just becomes N+N = 2N. And so on average, the population will have an equal number of children of each sex.
P.S. I will agree that Google's phrasing could have been more precise. But that is the case with virtually any math problem that is phrased as a problem in the real world, and I believe Google's intended problem is sufficiently clear that there is no real value in debating all its possible meanings.