Doubts? No. As an agnostic, I know for a fact that the question is unanswerable. So I don't worry about it.
There is something logically wrong with this sentence, but I can't figure out what.
That is quite a silly response. All questions are "unanswerable" in that sense, and anyone who has taken the time to think beyond a collge bull session discussion of theology/philosophy knows it. The validation of your own existence and that of the cosmos is "unanswerable." Yet you merrily go along accepting both on FAITH, every day. Indeed, your participation in this thread assumes you accept several unverifiable assertions: Your existence, the existence of the persons to whom you respond, meaningfulness and knowability of propositional truth. None of these things can be "answerable" in the sense you post above.
Are you asserting that you never worry about ANYTHING? Unless you are a poster child for zoloft, I think not. You are concerned about many things. Probably the same bag of crap that confronts all of us, including money, career, relationships, and your place in the web of those things. You have as little means of independent verification of those things as one does of the existence or non-existence of God, yet you assume they exist and predicate much of your activities on the idea that they do exist and have meaning.
If you want to question the existence of anything, that is your prerogative and I firmly support your right to do so, whether it be God, the Bible, the validity of dialectic materialism, or some vagaries of string theory. However, if you spout out some silly nonsense implying some issues are "answerable" while others are not, and you just don't worry about those which are not, then be prepared to have someone call that asinine yawlp the rubbish that it is.