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Why is double spending a problem. Suppose I have 1 bitcoin and I intend to send 1 btc to Alice and 1 btc to Bob.

Once I send 1 btc to Alice, UTXO of 1btc will be unlocked,transferred to Alice.No change is returned.Since Now when I try to send 1 btc to Bob, I have no UTXO to send it from. So the question of double spending is out of the question.

The double spending can be a problem when multiple transactions occur at the same time. If that is the case, why allow multiple transactions to occur at the same time?

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Double spending commonly refers to the situation where you send 1 BTC to Alice but you privately create a fork and on that fork you send the 1 BTC to bob. If your privatefork mines enough blocks to surpass the main fork (i.e you have the majority of hashpower or you are really lucky) you publish it and all the nodes consider it valid since it is the longer chain. As a result Alice loses her 1 BTC.

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