Occam's razor is attributed to the medeval philosopher William of
Occam (as I recall.) He said (roughly) "do not multiply hypotheses
unnecessarily." When there is more than one explanation for a
phenomenon that fits the facts and that is not contradicted, then
pick the one that requires the fewest (or simplest) new hypotheses.
So: given a fact: "there are currently no Unicorns" then either
1) there were never any Unicorns.
2) There were Unicorns, but the pixies scared them all away.
We pick (1) instead ot (2), because if (2) then we now need to
worry about the pixies.
"Extraordinary claims require extraordinary proof" is an
similar principle. If a claim is really weird, then
it's a lot more likely to be in error. Therefore, the onus
is on the claimant to be convincing, and not on the rest of
society to refute the claim. This is a practical matter:
if we waset our time on low-probability investigations, we
won't be spending time on more worthwhile endeavors.
Note that I'm now talking about science, not law.
If you claim not to have committed a crime, then our
society has decided that the onus is on us to prove
otherwise, beyond a reasonable doubt, even if the simplest
explanation is that in fact you did commit the crime.
Your crackpot theory has no such constitutional protection,
and it should not. (Not directed at you, Andrea. After all,
I'm the one withthe crackpot theory!)