Why Is There Something Rather Than Nothing?
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People use the same argument to "prove" the existence of God. The existence of anything can then be proved simply by including in the definition that it must exist. Example: Dragons must exist because I can define "dragon" as what is traditionally thought of a dragon, plus the claim that it exists.
Also you can't at the same time say that non-existence is ruled out on logical grounds, and then define it as something that's clearly possible, namely the absence of the universe. It's conflating an abstract concept for a physical one.