If someone states something they consider a fact, then, one can believe it's a fact, or not believe it/s a fact, so, if they say, I believe you are wrong, or, I don't believe you, they are saying I think you are in error, or even, I think you are lying. I believe believe is being used as a short hand for these possibilities. Do you know believe me? I personally, believe this to be the case, but you may not.
If someone states something they consider a fact, then, one can believe it's a fact, or not believe it/s a fact, so, if they say, I believe you are wrong, or, I don't believe you, they are saying I think you are in error, or even, I think you are lying. I believe believe is being used as a short hand for these possibilities. Do you know believe me? I personally, believe this to be the case, but you may not.