If someone says "I know I'm biased, but...", then I take that as a signal that they are expressing a personal preference, or some other harmless thing. I don't think this is necessarily something to avoid, because conversation is not usually about presenting evidence and argument. From the standpoint of advancing knowledge, conversation is mostly a waste of time. But it serves other functions.

As a point of contrast, in this forum, we mostly don't converse. We discuss.