Fine, but it's not what the statement actually implies. If I say "I don't drink wine", it could mean "I don't like the taste of wine", or it could mean "I am a recovering alcoholic and no longer drink wine", or it could mean "I have never and will never drink wine regardless of the taste". However, these positions are not necessarily implied in the statement "I don't drink wine", from which the only implication we can really draw is that the person saying it, for whatever reason, does not drink wine. In exactly the same way, you may equate "I don't believe in bigfoot" to saying "I don't believe bigfoot exists", but when someone tells you they don't believe in bigfoot, the only necessary conclusion to draw is that they don't believe in bigfoot, not that they believe bigfoot does not exist.
This is identical to saying "I don't believe in bigfoot", but not the same thing as saying "I believe bigfoot doesn't exist".
And those positions can be divided into two: accepting A and not accepting A. Where is the contradiction?