Why is car insurance compulsory here in FL?

"Her arm broke. She is insured with my man's insurance. The insurance company consented to purchase the doctor and hospital bills nevertheless the doctor's workplace never submitted the statement to the insurance company. There's evidence which they therefore are trying to blame us because of it saying we gave them the incorrect data and presented it for the inappropriate insurance provider. I have no idea where they believe we came up on an insurance provider we never had with info. Additionally they'd the best data if they charged our insurance for a prior case. Now a couple of years later the physician's office is attempting to get the money from us saying it's too late to get on our insurance. Can they are doing that? On a monthly basis we spend a great deal for health insurance