They probably reasoned that it would be suspicious to be traveling with a child with a different passport. My wife got the third degree from immigration in Australia in the early 90's traveling on her Canadian passport issued in her maiden name with our two children who had US passports.
My British mother had us kids listed on her passport to avoid just that. I didn’t get my own passport (American) til I was 16. I’m actually in the process now of getting my own British passport, by virtue of citizenship by descent (strictly for SHTF purposes).