People believe in witchcraft and lots of other things - including many horrible prejudices - just as confidently as you. There's a reason any scholarship, courts, medicine, and any other serious endeavors require objective evidence.
Imagine that - doctors, who have seen everything, have years of study, treat all those people, still require objective evidence. Anyone in IT looks for objective evidence - timing, stepping through code, etc.
Confidence doesn't correlate well with accuracy; in fact the more someone expresses your kind of confidence, the less I rely on them at all.
What if you wrongfully accuse someone? Does that matter? Are you responsible for the consequences of what you do?