Paradox unexplained

For the black hole information paradox I would expect
two seemingly conflicting results (as is necessary for
a paradox by definition,) e.g. like:

1) We know that information is lost because [...]
2) But also that it is not lost because [...]

Unfortunately I cannot find it clearly explained in
that way. To be honest, I cannot even find the first
statement clearly explained.

What I mean is: by using Kruskal-Szekeres coordinates
we can follow any molecule, or larger object, that
enters the black hole, and there is no clear indication
that it ever loses information at all! There might be
tidal forces tearing it apart, but that need not in
general destroy information and also that need not
happen at the event horizon (in fact the Schwarzschild
radius has no special local properties at all, as the
K-S coordinates prove). Finally, singularities may be
present somewhere inside, but we don't know the physics
there, so we cannot claim anything about what happens
to information at those sites.

Actually, for statement 2) I also never found a really
satisfying explanation, but let's leave that out, since
without *two conflicting statements* there is no
paradox anyway.

So why do people feel there is a paradox?!

--
Jos