obvious ("dumb") question about oracles and P vs. NP


This is going to sound idiotic, but this has been troubling me.

From the Baker-Gill-Solovay proof, we find that there is an oracle A
s.t. NP^A = P^A, and an oracle B s.t. NP^B != P^B.

Here is my rather dumb question: Why is it that the second inequality
doesn't prove that P != NP? If there exists one oracle relative to
which NP and P are not equal, shouldn't that imply, in a certain
sense, that there is some "difference" between NP and P? Relative to
the oracle B, NP and P are provably different. Why doesn't that
translate to a proof that P != NP?

I know that this is basically just my own lack of understanding of
oracle machines, but that doesn't bring me any closer to understanding
this.

Thanks,
Phil
.

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