All very logical, but logic doesn't warm the heart nor soften the pain of human beings.
This question I can answer from a personal perspective because I have inhabited both camps.
As a non believer I always declared that I would not believe in ghosts until I was confronted by one personally. I refused to fear anything supernatural until I experienced it personally.
To my utter astonishment I did have this experience of that which we call God (the Hebrews refused to speak the name) in the most unlikely setting. It was not in a lofty cathedral, nor atop a mountain gazing at the setting sun. It was in the auditorium of a hotel/motel where I was participating in an inservice for school councillors that lasted for 5 days.
I was there under false colours because I was just a science/maths teacher lacking even one lecture of psychology but the principal wanted to introduce a pastoral care program and she nominated me. The inservice mostly consisted of small group sessions in the motel rooms plus one plenary session per day in the auditorium. It was in one of the plenary sessions during an exercise called a guided walk that I had a most startling experience. Towards the end of it we were prompted to silently ask any question that came to mind and receive an answer.
Before you respond that I was under hypnosis, I will assure you that I was not. I once volunteered to be hypnotised by an entertainer and although I wanted to experience it, I failed to succumb. I resisted the suggestion. Apparently, I do not like losing control of myself.
When prompted to ask the question my response was immediate. Without thinking about it, a question seemed to rush up from the depths of my being. It was, "Am I a worthy person?"
Now you would think that I was looking for affirmation and you would be correct, but the answer was quite oblique. As quickly as the question was formed, the answer returned. The answer to my question was, "We are all unworthy."
My response was pretty much, "What the heck? Where did that come from?"
Two things I am sure of - that was not the answer I was seeking and that it came both from deep inside me and also from without.
From my days in Sunday School as a child I remembered the verse "...all have sinned and fall short of the glory of God" (Romans 3, 23).
This experience shook me to the core. I spent days trying to process it. I tried to explain it away using logic until I had another strange experience that was unprompted and unsought.
One night, less than a week later, I woke from sleep after hearing my name being called. It sounded like my mother calling me to wake up when I was a child. I was rather difficult to wake in those days. Instantly, without thinking at all, I answered, not with, "Yes, Mum" but with the words "Yes, Lord". Then I rolled over and went back to sleep.
The next morning I felt very different. I felt elated and relieved of a great burden. I remembered the bible story of the boy Samuel being woken from sleep by a voice calling him by name. The boy was in the service of the prophet Eli. The story can be found in 1 Samuel 3. I also remember the story of Saul's road to Damaskus conversion from a persecutor to a disciple.
I chose to respond positively to both experiences. I knew that I could rationalise both away using science and logic but I chose not to. From that day to this I have followed the path of faith, my constant companion on the journey has been that which has no name, but which many call God. As we say at the end of each Sunday service - "We go in God, and God in us".
Have I rejected my interest in science? Absolutely not, but I place my trust in something that science cannot and does not prove, nor disprove.
Am I happy? Absolutely yes.
Do I believe that the Bible is to be taken literally? I do not.
I just know that faith in God, by whatever name you choose, is not a mind thing.
It is about trusting with the heart.