Why should I negotiate the out-the-door price instead of the monthly payment?

Because a monthly payment can be lowered without lowering what you pay, simply by stretching the loan term, changing the down payment, or shifting money elsewhere. The out-the-door price captures the vehicle price, taxes, fees and add-ons in one number, so you can see whether you're actually saving. Agree on that total first, then compare financing. If you prefer to think in payments, confirm the price, term, APR and total cost behind any payment quoted to you.