Because very few states (and I don't practice in TN, so you should check your Secretary of STate's website, which often addresses this issue) allow most contracts to be cancelled in 3 days, or ever.
That's a commonly believed, but totally wrong, myth.
So unless your contract is one of the few kinds that can be cancelled, like home loans, home improvement contracts, gym contracts, etc., or unless the contract itself says so, you can't cancel it. And even if you can, the law or your contract will proscribe a certain method for cancellation, such as giving notice in writing sent to a specific address.
Car contracts are never among those that can be cancelled, so dealers use high-pressure tactics because they know lots of people think they can sign a contract and get out of it later.
There were probably prominent signs in the dealership that said there was no "cooling off" period, and they use those to defend claims like yours regarding people who try to get out of the contracts they've signed. They hope you didn't notice any signs or the warning in the contract itself, and you didn't.
Does this mean you have no argument? No, but it's not a good argument to mention the paperwork not being done, or the car not being delivered. If the contract you signed doesn't make any of that a contingency for the enforceability of the contract, then none of that matters. All that matters is you signed a contract and made a bunch of promises and you've got to honor that contract. That document spell out the parties' respective rights and remedies, so if you didn't read it, now's a good time (although a much better time was before you signed), or see a lawyer for help.
Avvo doesn't pay us for these responses, and I'm not your lawyer just because I answer this question or respond to any follow-up comments. If you want to hire me, please contact me. Otherwise, please don't expect a further response. We need an actual written agreement to form an attorney-client relationship. I'm only licensed in CA and you shouldn't rely on this answer, since each state has different laws, each situation is fact specific, and it's impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.