There is no reason to specifically appoint a woman to the FCC chair, if that is what the question implies, but there is also no reason a woman shouldn't. What is more important than considerations of gender is qualifications. The best person for the job should have it, regardless of all other circumstances.
The bottom line comes down to this, if a lady is qualified to do the job and is able to perform the functions there is no reason she should not have the job. I do not read one thing in the FCC that a women could not do if she was not well qualified.
A qualified woman, as well as a qualified man, can lead the Federal Communications Commission (FCC). Heading up an important agency like the FCC isn't a matter of gender as much as a matter of ability and qualifications. If a person is the best qualified for the job and has the greatest ability to carry out the duties of that job, gender should not come into the decision. Therefore, a woman can head the FCC, as can a man.
Of course a woman could and should be ABLE to head the FCC. However, she should not head the FCC just because she is a woman. She needs to have more credibility than just her sex. That would be reverse discrimination. A qualified woman would do just as well as a qualified man though, that's for sure!