If there already exists "a binary" then that says there are 2 states. "Non-binary" only means there are not-two-states. This could be unary (there is one kind of thing), trinary (there are now 3 things, the old 2 and new, secret 3rd thing), or really any n-ary set of n distinctly numbered things, so long as there aren't only exactly 2 of them.
The state of having two states and the state of not-having-two-states is itself a two-state solution.
Unfortunately, once you rule out non-binary as a third state, you collapse back into the original binary state. Thus, non-binary exists as a quantum superposition between states, as we fluctuate between whether or not being non-binary is politically correct.
We put a large box over the middle east and left a vial of radioactive material in there.
Now either Israel ignored it and freaked out about the box like everyone else or they immediately used it to make bombs and eradicate their neighbors out of view.
But nobody is in the state of having two states, though. People range from being in one state to "it's complicated", but how would you be in exactly two states?
I want to upvote the OP for presenting an interesting discussion but downvote them for being wrong. This presents a case for a non-binary voting option.
A singular like button would still only express one portion of my sentiment. A third option could be many things, none are sufficient: a none or 0 or neutral option is effectively not voting, a sideways arrow or maybe state, or mixed state would express indecision or indeterminism rather than mixed feelings.
Therefore, I propose that a second positive-negative axis is required. The addition of these "sideways" arrows allow expressing 2 kinds of sentiment: towards the post content, and towards the poster themselves. I will not specify whether left or right is positive nor will i clarify which axis (x or y) corresponds to which kind of sentiment. I'm sure this undefined behavior will cause no problems.