Let me put it simply. Whoever invented this argument is living in a fantasy world. It is one of the worst arguments ever invented. It is wrong about BOTH the "BIg Bang" AND conservation of angular momentum.
Lets go over the problems
1) The "Big Bang" does not start off with a "ball of matter".
2) The "Big Bang" theory does not propose that the initial singularity was spinning - let alone that it was spinning clockwise.
3) The "Big Bang" happened about 9 BILLION years before our solar system formed. The direction of spin will be a product of the formation of the solar system and later interactions (possibly including the capture of material from outside the system). And all this is completely in accord with conservation of angular momentum.
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