Approving an EMV transaction is actually a two-step process. Both the card issuer and the chip itself must approve the transaction. First, the payment request is sent to the card issuer. Once the card issuer decides whether or not to approve the transaction, it sends its decision back to the chip. The chip then has to make the final determination and finalize the transaction. The card needs to stay inserted throughout the entirety of this process.
While it can be frustrating or awkward to wait for the authorization to complete, it's definitely worth it for the increased security EMV provides!