When someone asks you how you are doing and then out of politeness you ask them how they are doing and they say don't ask, please don't ask what could that imply?

Either a) they have issue(s) and don't want to discuss it, or b) they are psycho and really, really want you to ask them all about their lousy life so they can describe it to you in excruciating detail.

Nip it in the bud. Respond to "how are you"s with "Fine thanks, you look well." You don't actually care how they are right?

Hi, mellymo1983!

In my experience, it usually means that the person isn't having that great of a time and doesn't really want to share how they're feeling. I usually take comments like that at face value. However, if I know the person really well and am concerned about their welfare, I might probe a bit further to see what's going on with them.

Thanks!