Title VII of the 1964 Civil Rights Act
§703(e)(1)
It shall not be an unlawful employment practice for an employer to hire and employ employees, for an employment agency to classify, or refer for employment any individual, for a labor organization to classify its membership or to classify or refer for employment any individual, or for an employer, labor organization, or joint labor-management committee controlling apprenticeship or other training or retraining programs to admit or employ any individual in any such program, on the basis of his religion, sex, or national origin in those certain instances where religion, sex, or national origin is a bona fide occupational qualification reasonably necessary to the normal operation of that particular business or enterprise.
Generally, there is nothing unlawful about a place of business having particular standards regarding who they wish to hire for a position demanding of certain qualifications. Afterall, there are many legitimate reasons as to why a business may choose to hire a woman over a man. However, it is the employer's responsibility to prove that under the circumstances, such standards exist as a bona fide occupational qualification and not an exercise of unjust descrimination.
Someone mentioned the Civil Rights case involving Hooters, which resulted in Hooters being required to hire men as "Hooters Persons". Hooters claimed in the lawsuit that the position of "Hooters Girl" served the purpose of providing "vicarious sexual recreation", which made gender a "bona fide occupational qualification" in their employee's line of work. The only reason that Hooters lost the case is that in their advertising, Hooters was described as being a "family restaurant". As the outcome of that case shows, actually proving bona fide occupational qualification is a very difficult thing to do in most cases.
If you feel that there was no legitimate reason for the secretarial position to have been denied to you, then maybe you should see an attorney. Even if the employer can provide a reason for such hiring "standards", there is still a chance that it would not hold up in court as a bona fide occupational qualification. I also agree that proving you were denied on grounds of gender would be difficult, unless you have some way of proving that you were denied the job for that particular reason. Afterall, the burden of proof first must fall upon you as the claimant.
I'm sorry that you were denied a job under such an unfair set of pretences. I hope that you do see an attorney regardless, as only they -- not GAF -- are qualified to properly educate you and provide advice in this situation. Good luck!