The larger the sample, the less likely there is to be a pattern than does not reflect an underlying structure to the data. It's true that with a large sample, a modest effect can reach statistical significance without being significant in the practical sense, but a pure fluke is far less likely to happen in a big sample than a small one.

Now for my question: did they use the number of months between a pair of births as a variable? I read somewhere years ago that the second of two boys born in close temporal proximity would be less masculine than the first, and in the case of two girls, the second would less feminine (or more masculine) than the first. They have the data; I wonder if they looked at this too.