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Although statistically impossible, imagine that two different private keys share the same public key. Would that addresses be able to create new Bitcoins? Let's say that private keys A1 and A2 have the same public key A. I use wallet B to send 1 Bitcoin to A. Both A1's and A2's wallets would show a 1 Bitcoin balance. Now both A1 and A2 send 1 Bitcoin to B at approximately the same time. Will B now have 2 Bitcoins, or would one of the transactions fail?

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There can only be a single spend of a transaction output, it doesn't matter if there's multiple private keys which correspond to a script. It is functionally the same as one private key signing two transactions, they can't co-exist due to the consensus rules of Bitcoin.

1

Since A1 and A2 have the same public key, it means that the network will treat them as one person.

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