Can the TSA make me remove my socks?

I always remove my shoes and wear my socks through a checkpoint because I am self conscious of my feet and have never been asked to remove my socks. Today at a TSA checkpoint, a male TSA guard asked me to remove my socks so that he can see my feet and make sure I wasn't hiding anything in my socks. I didn't set off any alarms and he made it sound like it has always been required to remove both your shoes and socks at checkpoints. Is there a way I can request a female guard privately watch as I remove my socks and allow me to put them back on after she confirms I'm hiding nothing in my socks? I think this male guard had some kind of foot and am not comfortable walking around in public barefoot and as I said, I have never been asked to remove my socks before and I fly often. Are you really required to remove both your shoes and socks? I've seen plenty of people who remove only their shoes and I've even done it and until now, I never have been asked to remove my socks.