Notice how the men did significantly worse on their exam scores after values affirmation. What's the explanation for that?

That difference looks to me to be within the margin of error.

Maybe the women who believed the data that men were better at math showed the greatest jump because they believed in data, and so had greater aptitude thereby?

Among the stereotyped group that most believed the stereotype, there was the greatest divergence between the effects of the two writing exercise. Your suggestion should predict that all of the stereotype-believing group would improve equally. Also, "they believed in data, and so had greater aptitude thereby"? It would be a lot less embarrassing if you just figured out and stated your true rejection of this study.