Nope, Dad is wrong. Full coverage doesn't mean what he clearly thinks it means.
It actually means, you have at LEAST state minimum liability coverage. You don't necessarily have any medical coverage, or lost wages, unless it's required. You don't necessarily have any rental coverage, or towing coverage. As far as the car itself, you have collision (who knows what deductible, it could easily be $1,000) and comprehensive coverages, but it only pays the ACTUAL CASH VALUE of your car. That means, if the sticker price was $17,000, and you paid $17,000, and financed $17,000 plus tax, title, registration, and put down $1,000 on your car, the second you drove it of the lot, it's now a USED car, and worth maybe $13,000. If you totalled it, you'd probably still owe about $4,000 after State Farm paid the ACV, PLUS, your deductible.
So dad is WAY WAY wrong.
The only time you can get rid of the gap coverage, is when the loan payoff amount is less than the ACV of the vehicle. Figure the ACV by getting the private party sale value from www.kbb.com. Not retail, not dealer markup, not financing costs. Private party used car value.
Don't take insurance advice from people, no matter how well meaning, that don't have a license to give you insurance advice.
agent 21+ years