That sounds illegal and, at the very least, it's incredibly disrespectful. I wouldn't continue to work with this company.

P.S. you don't have to have every qualification they're asking for. This is actually part of the reason why there's a gender gap in pay: because men are more likely to apply for (and get) jobs for which they're less than qualified, while women tend to only apply if they meet 100% of the requested qualifications. The list of qualifications is only a "wish list." When I realized this is how things worked, I started applying for jobs I didn't think I would get. And I started getting offers for those job. Unless it's a job that requires a license you don't have (such as a nursing job or a licensed social worker or something like that) if you think you could "do" the job, apply even if you don't meet the qualifications.