Hmm, while everyone is sticking up for our female lead, I'm with the director on this one. In real life, famous and popular actors are often handed a leading part. They may be beautiful people who are very talented in acting, but that doesn't mean you fit the part. Especially if you're very well-known with other movies, people might see the actor first and the role second. Take Emma Watson as Belle for example. She fits the part in theory, but in actuality, people just see Hermione in the 18th century.
If the director wants someone less widespread known for his own vision, I'd say that our lead is overstepping here. Being great at acting and being a fan of his work, doesn't mean you are entitled to be part of it. That's just being arrogant.