These feelings sound familiar.
I can only speak for myself, but this seems due to a shred of belief still in existence. My mind tells me that most of what they teach is wrong. My mind tells me that, judging by all the contradictions in the bible, God doesn't exist at all. However, part of me still believes everything. Many of us have been conditioned to believe certain things from birth, and it's hard to get out of that mindset. I think that's why many people are afraid to challenge the existence of God: They 'feel' his presence, but don't consider the possibility that this is due to years of brainwashing. They don't want to discover that everything they'd believed in was a lie.