What is the current theory about the connection between breast cancer and abortion?

No increased risk: The american college of OB gyn made this statement "early studies of the relationship between prior induced abortion and breast cancer risk were methodologically flawed. More rigorous recent studies demonstrate no causal relationship between induced abortion and a subsequent increase in breast cancer risk.".

Unrelated: Early retrospective studies suggested a link that has not been supported by more rigorous prospective studies. This is likely due to a retrospective bias, where women with cancer were probably more likely to be truthful with their medical histories than unaffected people, especially about as sensitive of a topic as abortion.