To believe something is possible, you must have some evidence for it. If you believe something without any evidence, you are dealing with arbitrary whims or claims.

If I claim there are tiny, sentient gnomes running around in my garden, I should have some evidence for that claim. If I insist it's possible without identifying any evidence, you would rightly conclude I'm insane.

You evaluation of evidence, or your logical process, could both be mistaken and so you might believe things that are not true. But if your belief is based on evidence, you can test it and revise your understanding.