To me, logic was a rational review of the evidence. To believe in the God of the Bible I would have to accept things I've never encountered and, as a child of the 60's, I was very skeptical of what others told me to believe.
Evidence is defined by what can be measured by the five senses.
I would not describe you as skeptical. Compare how you acted during Covid and how I acted. I refused to wear masks, refused to stay inside, refused to wash down all my purchases after coming home from the grocery store, avoided the mandated vaccine(s) at the workplace. What I did do: Went online to see what worked during the Spanish flu (1919-1918). Wash hands frequently and change towels, drink plenty of fluids, vitamins with zinc do not hurt, sun, fresh air, rest, and exercise. I also looked up the efficacy of face masks (it was at best a placebo), and if those who were recommending face masks and vaccines were investors in pharmaceuticals. (Never let a crisis stop the already rich and powerful to milk said crisis for more wealth and power.) Clearly I'm the more skeptical (and probably the more cynical).
I also challenge your "logic". Depression and pain are two conditions that can have no physical measurement (or even symptoms) but I'm betting you always accept a person's word when they say they are experiencing pain (even mental pain) or feel depressed. But let people (and there have been millions down through the ages) tell you they experience God (or angels) and you dismiss them out of hand.
Example: More than half the population believe in God. Slightly less than half the populations goes through childbirth. This half testifies that childbirth is painful. What physical evidence is there for this pain and how much pain there is? Perhaps your mother even told you that your childbirth was painful. Were you, being skeptical at age twelve, disbelieving and asking your mother to produce evidence that she had been in any pain at all? I'll bet you accept painful childbirth as fact, even menstrual cramps as fact. If someone tells you they feel suicidal, I'm betting you will rush to bring help to them, even though you have no "evidence" only testimony.
Yet, when you are given testimony, experience, and others' knowledge of God you dismiss this out of hand. Why? Expectations. I'll bet almost everything (not my first born child) that because faith/religion/God call you to a greater expectation and you don't want to be bothered. You wanna do what you wanna, not what service God might call you to provide for Him and others. The other thing that crosses my mind is that most of the time you actually feel a responsibility to meet the expectations of others--and meeting God's expectations crosses the line of what you feel is fair to you.
Okay, all this being said, I am not playing a psychologist, have no knowledge of psychiatry, and definitely cannot read or even look into your mind. I am presenting only what is crossing my own mind, hoping (if you feel irritated after reading that diatribe) you will take a beat and be patient with me. Thanks!