I like your question.
Dog person. Although until about age 30, I was a definite cat person because of my two great cats, a calico manx and a fuzzy himalwayan-type of cat (Kabi and Angelo). When they passed, I knew it would be a while until I got another cat.
The way I became a dog person was that one day, I was at the animal shelter searching for my son's chihuahua, who had gotten out of the yard, and I came across a rat terrier. She wasn't adoptable yet, but I knew i was going to come back for her. When she became adoptable, I went back for her. That was in 2000. Her name is Beckie. Then about five years later, I adopted another rat terrier, Hankie. Two years ago, my son brought another rescue home, a papillon, Tina. They are all such great dogs and I don't know that I will ever stop being a dog person now. To me, dogs just make better pets and have many abilities which cats do not. No offense cat lovers! : )