I know a few people like that, can't abide the thought of pet hair or whatever, I get it, and there's others who are allergic to cats or pet hair and so on. All understandable.
For me, I couldn't imagine my life without my cats (have only one currently) and they bring an amazing amount of happiness into my life; more than most people to be honest. Of course, it is additional work, keeping the house in order as I also have a need to have an immaculate house...but it's worth it for me, the benefit outweighs the loss in time.
People have the right to choose I guess, and there's no right or wrong to it, there is just the individual's way.