I wouldn't find it offensive.

Parents take one heck of a risk initially with a provider. Sure, due diligence is performed with police checks and references but at the end of the day, it's quite a leap of faith handing over your child to someone who is essentially a stranger.

I think, in that situation, it's perfectly normal to ask a child about their day. And during those conversations, some topics might arise which are very important.

"What did you eat for lunch today?" - Dry cereal and water, KD, processed crap which the provider promised she never feeds.

"What did you do today?" - Sat in front of the TV and watched Ellen and Judge Judy, when the provider promised there is no screen time.

"Cameron had a time out today Daddy."
"Really? Why? What did he do?"
"He got mad because he didn't want to share the toys. He threw a dinky across the room and it broke Rachael's picture"
"Did Rachael get mad."
"No but she wasn't happy. She said Cameron had to sit in time out whilst she cleared up the glass and all the rest of us had to sit on the couch off the floor so we didn't get it in our feet."

See - conversations evolve and it's perfectly reasonable.

You can choose to be offended but to be honest, it seems rather silly as no one gets to determine the thought process and conversations another person may and may not have. Since it's not in your control what they discuss, why feel anything about it?

Surely it's a good thing that they are sharing with you that their child views you as calm and fair vs an over-reactive, emotional wreck?

I'm not sure what you mean by "after all I do for this child I'm helping him in potty training". LOL Surely that's just part of the job for this age group, like helping them put their mitts on? It's hardly going out of your way but a fundamental part of the role of caring for children.

this family makes me think that he doesn't learned anything here and that they do the job at home I don't believe it at all I have teach him many things and they find it hard to accept it, and for some reason they make me feel that they are afraid of me terminated them so I don't understand! please any advise
This makes no sense based on the information you have provided.

Do you mean this family makes you feel that he's not learning in your care? If so, what have they done for you to draw that conclusion? Surely a father asking about your temperament isn't making you feel like this?

What has this child learned since being with you?
How long has this child been with you?
How often is this child with you?
And why do you think these parents believe he's not learning?
And, just as relevant, - you seem to be annoyed that this parent has been really direct and honest with you about the conversations they are having and yet you think they are implying other things rather than being equally as direct?

Sorry but as posted, there's no information to offer any advice with.