He probably overlooked her because she's a lot like Stan.

I think that the lesson is that the twins (Ford/Stan and Mabel/Dipper) are stronger when they are united. Ford without Stan was tricked by Bill and had no real friend to trust, Stan without Ford fucked up his life and became a fraud, Dipper without Mabel becomes too self centered and Mabel without Dipper doesn't think thorughly.
Dipper without Mabel would never be at his full potential.