If the spin of planets, galaxies, etc., came from the fact that the big
bang matter was spinning when it blew up, then the conservation of angular
momentum demands that all planets be spinning in the same direction.
Since some planets and moons spin in a retrograde motion, the big bang is
disproved.
The claim is based on so much ignorance and so many misunderstandings
that it is hard to know where to begin.
The big bang was not an explosion. Space itself expanded (and is
still expanding).
The big bang is quite a different subject from the formation of
solar systems. Rotations within the universe are not expected to
be related to any rotation of the cosmos. Galaxies probably arose
from slightly denser regions of the early universe, which coalesced
and combined due to gravitational and viscous interactions. Since
these early density fluctuations were apparently random, we expect
galaxies to have random orientations. Solar systems within
galaxies have still different origins and additional random
influences on their orientations.
Conservation of angular momentum doesn't require that everything
spin the same way. It requires that a change in spin in one object
be compensated for by an opposite change in spin in one or more
other objects. Retrograde planets are
not a violation
of angular momentum because other bodies in the early solar system
could account for the compensating spin.
If the big bang were an explosion, we would expect different
spins.
When something explodes, pieces fly out spinning in all directions.
