No. I began with equality. You spoke of inequality afterward while you believed you were correctly referring to my analogy.
See, equality is inequal to inequality.
Inequality doesn't make any sense for your purposes, especially if you try to put it in the form of my original analogy:
1 does not equal 0 ... yeah, and? There's no symmetry there. What can you learn from this? Your association between symmetry and inequality is an invalid assertion you've naively made, in addition to your original speculation regarding symmetry and 'nothing'. I mean, that's completely ludicrous!
If 'nothing' is symmetry, then what kind of symmetry is 'nothing' ? Does this idea apply to my analogy? Let's try. 1 = 1.
Is that 'nothing' ? How so? Clearly, you're just tossing around arbitrary logic. Also, symmetry is definitely not the only property you can abuse... there's a lot of arbitrary logic you can employ to drag yourself nowhere. Once you're satisfied with this useless idea, you're free to enjoy it as much as you would like: only leaving it behind and forgetting it as useless at it is, regardless of my criticism. I would love to see more interesting results come from this idea.
Ultimately, my point here is that you clearly are not working with a rigid concept. Your vague conception has already deceived you into asserting that there exists a clear bridge between nothing, symmetry and... inequality? Ooops! You could have only meant equality, which demonstrates how your own grasp is too vague to be handled coherently even by yourself.
This is how the field of philosophy is being abused by naive and radical thinkers who only thought they couldn't fit their ideas into the mainstream fields... which is not true. It's a common and fundamental problem with the way these "philosophers" try to approach theory. They believe it makes sense to dance in their own theory without any valid or coherent basis. A lot of people don't know how to appropriately establish new ideas, and this leads them to wondering why their brilliant light-bulbs can't screw in anywhere but philosophy; the only field which appears to accept their desperation.