As I understand it, the Hundred Year's War started back in the 1300s when Edward III of England claimed the French crown by right of inheritance from his mother Isabella, while the French insisted that the royal succession cannot pass through a female.
In the Wars of the Roses, it seems like we have a similar situation: The Lancasterians were descended from a younger son of Edward III, and the Yorkists were descended from an older son, but the Lancasterians said that their claim was better because it was a direct male descent.
If, then, the Lancasterians were committed to the principle of male descent when it comes to England, why did they continue to claim the French crown based on female descent? Were they simply hypocrites? Or did they have some clever explanation?
They didn't see the contradiction. Henry IV and V pressed Edward III "legitimate" claim to the French throne which they, as his descendants still held. Meanwhile their rule had been ratified by parliament with the people behind them. As far as they were concerned they were legitimate in both respects. We might call them hypocrites today, but that's a modern value judgment on some cut throat dynastic politics.