Theism is a positive claim, the idea that something called a "god" has some form of existence and an effect on the world. The burden of proof lies on the person making the positive claim. It's the theist's job to sell their idea of god. We're atheists because we simply aren't buying it right now.
Imagine you answer the door, and find it's a salesman with a box covered in question marks. The first thing he does is ask you is for a good reason to not buy his product. That's what it's like to be an atheist.
1. Every theist has their own definition of "god." I don't keep a list of all of them. To put the exchange in other terms:
Theist: "What proof do you have that god doesn't exist?"
Atheist: "Which god?"
And even then, the answer isn't clear: Some Christians, for example, believe in a fire and brimstone god while other Christians believe in a peaceful, merciful god.
2. The burden of proof is on the 'salesman' to convince me his product is worthwhile, and to do that, he has to be able to define and demonstrate it to someone. I don't need to have a disproof. He needs to provide proof that his product works. Until I find a god who has predictable, repeatable effects on the universe, I'll simply file them all into the same drawer as other unproven entities like unicorns and psychic powers and do something more productive or entertaining with my life.
3. A lack of belief in something is supposed to be the default position in logic before evidence is presented. Theism has not earned this position due to its merits: From where I'm standing, theism is falsely elevated to the default assumption because of peer pressure, fashion, tradition, and other social pressures. I don't assume that those things automatically follow logic because I know human beings can rationalize just about any mistake they make with logical fallacies.