What does it mean when you claim someone on your insurance policy?

My son had a dental appointment the other day and he was referred to get some dental surgery done, although he needed a specific benefits card. I had went down to the social services (government office) to ask for a temporary print out one til the actual one gets delivered. They asked me if my son was on my claim and I said yes. Now I wasn’t thinking insurance I thought they were asking about EBT haha, sorry it’s just it’s the same office I went to file for EBT and I remember claiming my son as a dependent so that’s what pops into my head with them asking that. They said he’s not under your claim. I said are you sure? (Because I was still confused of course thinking they meant EBT) they told me to wait, they talked to another worker and told me he’s under his dad’s insurance claim, then they told me to wait to see somebody. I got called into the back and was told to verify all of my son’s information as well as his dad’s, and this was awkward for me because I don’t know if his dad’s information is still what I know, and apparently it wasn’t correct. I wasn’t able to receive my son’s temporary medical card. Since his father is a nutball whenever I talk to him, I already know I’m gonna look crazy when I ask him why did he add our child to his insurance..

I only have a problem with this because I had no idea of adding a child to my insurance, my son has his own medi-cal and card I don’t see why he was added to anyone else’s. I don’t know about claims like that. The last time his dad ever claimed him was on his taxes and he used all those child credits on drugs. I just don’t know what’s up with it and I can’t ask questions I already know won’t be answered. Now I’m just upset because he’s not even the responsibile parent taking our child to any of his appointments, I am, and I can’t even access anything. Great.

I guess my only question for you guys is what exactly is claiming someone on your insurance and what does the parent benefit from it, his dad in this situation? To me, co parenting, this comes off very sketchy.