That brings us back to my previous observation that there are many different standards of evidence. Science requires objective evidence founded on demonstrability, the courtroom another, sales and politics another. This is because demonstrability is applicable to very few things in life - particularly over things which you can control. Thus restricting yourself to this alone is not only outright impossible but also implies some degree of addiction to being in control. So for most of life we must use standards of evidence which are considerably weaker than what is demanded by science. And this is not just a matter of going with our best guess, because another factor playing into this is the fact that while science requires objective observation where what you want doesn’t matter, life requires subjective participation where what you want is central.
The reasonable compromise is thus to recognize the line and know when your decisions are subjective and do not pretend otherwise. And then you acknowledge the superior epistemological status of conclusions which are founded upon objective evidence. For religions this means that in order to be reasonable they must accept the correction of demonstrable scientific findings.
As for the question, why believe? Well people have a great many different reasons. Here are mine.