This isn't a issue from anything coming from the Torah. Rather, a dislike of dogs likely stems from anti-Semites in Eastern Europe having their dogs attack Jews, and later the use of dogs by the Nazis to keep concentration camp inmates in line.

However, there's is some connection to cleanliness issues also. Some people claim that the Jewish home should mirror the historical Temple in Jerusalem and thus should not have any non-kosher animals in it at all. See this essay which discusses this in more detail.