How does one really know anything about another person? You ask. Fairly simple. Would I suggest doing that? No. Not in a million years, but that is how you would know.
The dog mom trend is more based on the want of a child but not wishing to have one so they supplement it with a pup. It was not uncommon for the traditional nuclear family to start that way some 20 odd years ago. Marriage, puppy, a year later kids. Now it is all fucked up. That is besides the point. Often, but not always, these women call themselves dog moms because they see themselves as the mom and the dog the child. It is like asking if single moms with sons are into incest, highly likely they actually are not.
The other thing you mention is the large dog aspect of it all. Chihuahua's at one point were all the rage. Almost every Hollywood female had one, hell even Taco Bell had one as a mascot. Like with all trends it hit like wild fire but once it calmed down it normalized again. Some like big and some like small. It is just a personal preference indicating nothing more than what kind of dog you like or (depending on where you live) the kind of dog your housing allows.
Hope that helps.