Ok, imagine the original assertion was “All square numbers are even”.

I only need to introduce a specific example/constraint to disprove the original assertion: 1

My introduction of the example/constraint is directly relevant to disproving the original point. That is the whole point of introducing it, so it is absolutely not orthogonal.

If you then remove my constraint (1) and say: “but 4 and 16 can both be square numbers”: Sure you're not wrong, but that also has nothing to do with why I introduced my example in the first place, nor does it invalidate my example, and is thus completely orthogonal to proving/disproving the original point.