auto accident

What is the name of your state (only U.S. law)? florida
I was in a rear end auto accident, the insurance company wants to right off the car, I want to get my car fix and keep my car, What is my legal rights on this issue.

Insurance companies are not required to fix your car. They can fix your car if it is cost effective; otherwise, they will total it. There is no way to force them, for example, to pay $5000 to fix a $3000 car. Companies will typically only pay repair costs up to a set percentage of the car's FMV, as set forth in the policy. For example, the policy may stipulate that the car will be totalled if repairs are 75% or more of the car's FMV.

You CAN accept settlement for your totalled car and retain it with a deduction representing the salvage value. But this almost never makes financial sense, since you will THEN have to repair the car, and then jump through several hoops before you will be allowed to register and drive it again. And then, you will have a salvage title, which means the value of the car will be cut in half. So unless the car was already in pretty bad shape, and the current damage is only cosmetic, it will end up costing you more to keep it.