Ibn Taymiyyah wrote:The existence of anything is either:
This goes against the concept of God.
So we are down to two options: 1) Obligatory 2) Impossible.
You must really get Aristotle and Thomas Aquinas out of ur mind!
I'll make a move to your side without any cynism nor irony (yes i'm sometimes able of this

- you just have to trust my words when i say this).
OK, let's assume God exists, He's almighty, has no limit whatsoever and is 'obligatory'.
Do you really think that such a powerful
Being (i cant think of any better word) has such a short mind to always think in "yes/no" terms?
I mean, this kind of reasoning comes from Aristotle but where Thomas Aquinas was wrong is that he applied Aristotle's principle of third excluded (one thing cannot at the same time be and be not) to metaphysical objects (God's existence mainly). Aquinas was a very good theologist, a very good philosopher, a very good helenist no doubt about it and very good at rhetoric, so whether he misunderstood Aristotle (which i really doubt), or tradition misunderstood Aquinas. Aristotle's principle was used for physical objects, for sensible objects... he used it in his natural science works, not in the metaphysical ones. The weakness of Aquinas is that he tried to combine both Aristotle's method to with Plato's metaphysical thoughts... of course those couldnt match. When Aristotle says "what we cant see is, by nature, black (because no light is reflected from those objects), or no light coming from those objects can reach our eyes" he speaks out of experience, on material and physical subjects (those lines are from Pseudo-Aristotle's
De Coloribus 791a15). Now when Plato tells us about the Supreme Good, the bright Sun of Republic VII, he speaks of metaphysical objects which dont have any physical existence, u can whether be a believer or not. Aquinas, after Plotinus and Augustinus mixed both giving Christianity a "scientific" background trying to prove the umprovable.
My point now, is quite simple, God is almighty, we are very limited (both physically and intellectually). This we all agree (if we agree on the existence of God, but that's the first assumtion of this post). How, then are we to explain something so far beyond our reach? What would be the use of explaining it? I understand why ppl try to understand Nature and natural objects (physics, biology, genetics, etc.) because we're part of it and it all belongs to the same level of understanding and it can help us understand why we live (not the esoteric reasons for life, karma, divine purpose etc.), how to live better etc. I just cant see the point of trying to understand a Supreme Being however u wish to call Him/Her. What would it change to our life? An new area of slavery (slavery can assume many a face, worship, terror, sacrifices...). No. If there's someone/something above me and He/She wants me to know He/She's here, He/She just has to give me firm proofs (i know i've read the answer to the proof thing on the other thread but didnt answer this yet, i shall when i have some more time), and tell me clearly what He/She wishes me to do. If not, i have no reason to "bother" with Him/Her since He/She cant affect my life and i cant affect His/Hers.
So to get back to ur first "question", i dont think it's our job to try to find out whether God is "obligatory, Possible or Impossible". U can believe He/She is as such or not, but He/She's so much more complex than what we will ever be able to understand, it would be very arrogant to try to label Him/Her in such a simplistic way, so no, being agnostic is just not illogical at all, it's being able to consider other levels of logic which we cannot even dream to grab.
Of course it's not you i call "arrogant" it's the centuries of theology (would they be Jewish, Christian, Islamic or whatever else).