Since no one is objective, I am unworried by that charge.
It is certainly true that nobody can be wholly objects but that doesn't stop us from trying to be as objective as possible, especially on subjects that connect to science or mathematics and logic. In fact, if your claim to have made a "logic statement" was not an attempt to claim a degree of objectivity, then what
was the point?
The ppoint here is that you are effectively pursuing a category error in terms of the levels of meaning in the discussion.
What category error, specifically?
It's a sort of reverse mistake that people like William Lane Craig and Deepak Chopra make...
Unargued assertion.
No one's language use is purely on the theoretical physics level, nor could it be...
So what? You made a statement that contradicted well tested science, namely that existence was a "time based concept", whereas we have to conceive of the existence of the space-time manifold before we can get to time, and even then we have a relative, rather than absolute phenomenon. According to current tested science, your statement was simply wrong.
You then made another claim that "conceptually" we need time for existence and non-existence, which is directly contradicted by mathematics (and therefore logic). Not only can mathematics construct timeless notions of existence but there are physical hypotheses (e.g. loop quantum gravity) that construct (space-)time from more fundamental concepts.
No amount of talking about language, alleged non-objectivity, or accusations of undefined category errors can make these facts go away.