Why people keep saying "My Doctor , My Attorney , yes , when they have to pay for them services ?

Do this means people are out of they minds or are really dummies when they talk ?

Can I get a nice explanation to this and that ?
Well, I'll give you the nicest explanation I can, given that you're question isn't exactly clear.

"My Doctor" is easy. Whichever doctor you go to, YOU are ultimately responsible for the bill, you ARE paying them, one way or another - either out of pocket, or assignment of benefits.

"MY attorney" - also not too bad - as an attorney represents YOU in court. As opposed to "the insurance company doctor" or "the insurance company attorney" or "the other guy's attorney".

Attorney's can work for either side, and the same with doctors. So that's how you distinguish between the guy working on YOUR side, and the guy working on the OTHER side. Plus YOU PAY THEM BOTH, one way or another.
when you pay for it, doesnt it make it yours? Plus, you hire them to represent/treat you. You are thier client (so they can claim you also) just as they are your representative/doctor.

Answers:
Because when you go to a doctor continually they know you and they know your medical history and you develop a patient/physician trust relationship, so really it is "your doctor".

Same for a lawyer, if you use one often or are in the middle of a case with one it is "your lawyer".

Is that what you were asking? Your question was all over the place.