Turns out that kids -- gasp! -- kids don't just blindly listen to what their parents are saying. They watch what their parents are doing as well. Parents may say all the right things about gender equality, but if they display more traditional gender roles, their kids are going to pick up on it. Especially the daughters.
Girls whose dads don't help out around the house reported aspirations to female-typical occupations like stay-at-home-mom, nurse, or teacher. Girls whose dads do help out around the house are more likely to report aspirations to work in business and leadership.
Now, I want to be careful here not to fall into the "being a successful feminist means being a business mogul" trap. Of course the occupations of nursing, teaching, or staying at home for the kids are important and valuable contributions. HOWEVER, I think we all want any human child's career aspirations to be motivated by a perception that all options are open to them, not influenced by the implicit demonstration of traditional roles.
So, dads, listen up. You want your daughters to actually think they can be whatever they want? Pitch in around the house. What you do tells them a lot more than what you say.