LOL. Maybe that's why I keep getting slapped by women.
Actually, when you said that you weren't a native English speaker that got me thinking and something suddenly occurred to me. English is very strange, as you say. So strange that I can see one meaning of "believe" that may have confused you especially if you derived an understanding of it from a dictionary rather than a native English speaker. You may or may not be aware of this already but I thought I'd mention it in case it is the source of our disagreement.
Believe can sometimes be used to indicate almost the exact opposite of it's primary meaning. It's rarely used by Americans I think (although I'm sure they would understand it) but is used in England sometimes but it's a slightly archaic usage now. The reason I haven't mentioned it before if that the context of our discussion absolutely rules it out as being the intended meaning of the statement "I believe God does not exist" or suchlike and I didn't know you weren't a native English speaker and so it was something I thought would be obvious to both of us as irrelevant so that it didn't need mentioning. The rules of this usage of believe are very, very subtle, but a native English speaker (a well educated English, English speaker, at least) would instantly recognize when this meaning is not being indicated. And as such I'm telling you, it doesn't help your case, so don't get excited LOL.
Believe can sometimes be used indicate suspicion, very weak suspicion or even serious doubt. For instance you might ask someone where your car keys were and, if they had a vague idea they may have seen them in they kitchen, but certainly didn't know for sure, they might say "Erm, they are in the kitchen, I believe". or "I believe they are in the kitchen". It is often used in this way to indicate, not belief, but real uncertainty. It's almost a way of saying "I suspect they may be there, but I really don't know, so please don't take my word for it". Usually the tone of voice, word emphasis and facial expression is what indicates the degree of doubt. Now, the context and sentence structure of statements like "I believe God does not exist" totally rules out such a usage, but it's possible that if a dictionary listed such a usage that this may be where you derived your beliefs about "belief" and what it can indicate. Just a thought.
I had no idea you were not a native English speaker, which says a lot. :)