Me saying "gods don't exist" is just another way of saying "Those who believe in gods haven't proven they exist".
The burden on me isn't to prove gods don't exist. If 'negative proofs' were how we operate, then it would be on you, or anyone else, to prove there isn't a island of magical rainbow unicorns in the middle of the Atlantic Ocean and we'd all just have to believe that such an island exists, since none of us is able to prove every square miles of the Atlantic Ocean isn't inhabited by magical rainbow unicorns.