Many times, dogs are a non-issue when you meet someone special. In the beginning of a relationship, it's about discovering one another and enjoying time together. Many people are willing to put the little things like whether or not they like pets aside when they first start dating and then a short while later, their true feelings come out. If one person loves animals and the other would rather be without them, this can be a huge source of contention for the relationship.
I remember watching Keeping Up With The Kardashians one time and there was a scene where Kim's fiance Kris introduced her to his dogs. He was very sure she would warm up to them and then you see her saying to the camera "I love dogs but love them from a distance". When I saw that, the first thing that went off in my head was "RED FLAG". I was hoping that it was something they would overcome. Well, you know the rest.