Because the CLIENT doesn't know for sure if you still have the coin.
It doesn't need to.
If it is not fully synched, it CAN'T determine if the transaction is valid or not
It doesn't need to.
It just needs to broadcast it and see what happens.
- which is why a WELL WRITTEN wallet would not let you create such a transaction.
A well written WALLET (that creates transactions for you) shouldn't create invalid transactions.
A well written network CLIENT should allow me to communicate with the network and should broadcast what I ask it to broadcast. It can have safeguards that prevent me from accidentally creating a denial of service attack or other things that I might not want to do, but but should allow me to turn those safeguards off if I WANT to be able to do something that the client typically prevents.
Note that most wallets are built with the assumption that the wallet is in control of the private keys that the wallet knows about. If a user chooses to do something that isn't supported by the wallet (such as porting those private keys to other wallets or manually creating their own transactions), then the wallet may allow you to try to create a transaction with bitcoins you don't control any longer. The bitcoin network will reject the transaction, but even with a fully synchronized wallet, if you've ported your keys elsewhere, it would still be possible to create invalid transactions.
