Sorry, I didn't see this, else would have responded sooner.
Perhaps it's too late now, but for what it's worth...
Assuming your logic of infinite regress is true (for the sake of this discussion) that tells us nothing about the pre-existing agent of change. It certainly doesn't tell us that said agent requires women to wear a head covering. Religion makes (in general) more specific claims of the agent than can be supported.
I have no need to try and reject your logic, for the same reason I don't bother arguing with Deists, pantheists or panentheists. If there is an original cause, and you want to call it God, that's fine. But once you start defining God, and God starts impacting on how people behave or how they expect me to behave, I expect more of a rationale than 'infinite regress' to explain why.
While I respect what you are saying here, it is somewhat disingenuous for him to use an argument that can easily be (and has been) refuted a hundred times before. The fact that he does not understand the refutation should not cause him to use the same argument again and again.
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Unfortunately the analogy is wrong. In your analogy there still remains a time when neither A nor B is running. However a
beginningless system (A,B) where
1) A is running because B is running
2) B is running because A is running
will have
no first moment where either A or B was stationary.
It neither has nor requires an initial condition. In mathematics and in real life,
an infinite series or a set is a fundamentally different category of entity than a finite series or a set. Unless you understand this, you will be stuck.
I will add to this. Very simply a binary system (A,B) where
1) A runs when B runs and
2) B runs when A runs
will have
two stable configurations.
Configuration one is when both A and B
are stationary for infinity.
Configuration two is when both A and B
are running for infinity.
Both are perfectly stable and consistent configurations. Your
logical mistake is to believe that somehow the state of rest must be a more natural state than the state of movement, and hence configuration two must have a beginning point.
This is false. Both configurations (A,B at rest) and (A,B are running) are beginningless and endless configurations and are
mutually exclusive. They cannot transform from one to the other and they have no beginning or initial condition. Both configuration one and configuration two are perfectly possible ways (A,B) can exist and neither is more likely than the other.
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