Perhaps "I" am
"im", the centre of "time" (note also that "im" ~= "I'm" ~= "I am")
and "me", um, is
"possible" because if something is a thing then it must be possible
so that "we", errrm, is
"impossible" (by combining the two).
this doesn't seem to lead to any explanation of the "it's" in the title so I will be extremely unsurprised if it's not OP's intended answer.
im/possibility would work about as well as im/possible, and that does at least contain an "it" which might somehow lead to an explanation of the title.
Some other possibilities along similar lines (for the benefit of others, possibly including my future self, since I need to go to bed now):
The first one might instead be the centre of "axis", so "xi" (which forms part of words like "exist" and "nonexistence", which might be useful); or "t-axis", so "x" or "axi"; or just "line", so "in". The second might be any one of many similar words -- e.g., real, actual, existing, thing -- or, taking "nothing" more literally, might be "hing". I don't see any combination of these ideas that does any better than what I have above but, e.g., we could make "in/existent" this way. If we could make the first yield "not" it would play well with "hing"; if we could make it yield "un" it would play well with "real" or "reality".
As for the (revised) title:
the most obvious way to read it is as kinda giving away the answer: it's (i.e., the answer is) isn't (i.e., something that means roughly that) and (i.e., next to, or inserted in, or something) does exist (i.e., something that means roughly that). So e.g. if we could combine AIN'T and IS to make something suitably indicative of nonexistence, that would do. Right now, though, I don't see a way to fill the blanks so that this actually works. (And of course my interpretation may be all wrong.)