Such an important point.
All the characters we create are just facets of our own personality. So if we don't connect / engage with our characters, we don't connect with ourselves. And if we don't connect with ourselves, we can't connect with our audience.
I think we have a resistance to connect with our characters, which is essentially a fear of connecting with ourselves. If we connect with ourselves, we will have to face all the less-than-ideal aspects of our existence (in Jungian terms, our shadow).
So it's tempting to see ourselves as the protagonist of our story, but not as the other characters as well (especially the antagonist). And that blindered perspective (in my limited experience at least) tends to lead to a very shallow, uninvolving story. I think that the more you can identify with your antagonist, the more you can plumb the depths of the story that you need to tell.