Most dealers want to finance the vehicle they sell you, as they make a nice commission from the bank.

Never tell the dealer upfront, that you will be financing it elsewhere, or that you are paying in cash, as they will charge you a higher price to compensate.

About the "no prepayment penalty" that’s following the law. But, car loans like mortgages are so heavily weighted towards paying off mostly interest in the beginning, before significantly paying down the principal.

If you take the dealership’s financing, and refinance it a month later, you will be paying dearly….which is why they told you to do it.

As others here have said, find another dealer!