Modern philosophical legend, Adolf Grunbaum, considers the question, Why is there something rather than nothing? to be a pseudo-problem, and the theistic response to the question to be a pseudo-explanation. I would agree with Grunbaum on the latter, but I think that what Grunbaum dubs as Leibniz's Primordial Existence Question (PEQ) does pose a legitimate philosophical problem.
If we can equate nothing with the empty set and something with a non-empty set, (not a trivial assumption, given that mathematics extends beyond set theory), then it is significant to note that whilst every set contains the empty set as a subset, the converse certainly isn't true. This asymmetry can be used, I suggest, to construct an answer to the PEQ.
Because every set contains the empty set, the existence of something is consistent with the proposition that everything logically possible does actually exist. In contrast, the existence of nothing is clearly inconsistent with the proposition that everything logically possible actually exists; the existence of nothing excludes all other possibilities.
So the PEQ, Why is there something rather than nothing? receives the answer Because all logical possibilities actually exist. Needless to say, however, this then invokes the further question, Why do all logical possibilities actually exist? This can, in turn, be answered by equating actual existence with possibility, i.e., with absence from contradiction.
In particular, mathematical objects and structures exist because they are free from contradiction, and the physical universe, if identified with its mathematical structure, exists simply by virtue of the fact that that mathematical structure is free from contradiction.
Adolf Grunbaum Leibniz Nothing Something