That might have been a question to the people who invented the zero in mathematics. I guess we should just presume nothing exists, if we want to use the zero.
I don't think it's inconsistent for nothing to exist, and something to exist also. The relationship between nothing and something is a chance. What's the chance of it raining today? Will rain come into existence, or will it remain nothing? So you see, if there wasn't nothing, then everything what happens would be predetermined by what is, and there would be no chance or choice in it.
regards,
Mohammad Nor Syamsu