Because Longest chain is more accurate, since using Proof of Work implies the longest chain would have more work.
But, a chain can be longer than the current one with less work. The difficulty is what determines the correct chain. Someone may choose to mine 1,000,000 empty blocks, but if they're all mined with a difficulty of 1, the chain will be rejected. So saying that the longest chain is the correct one refers more to the chain's height rather than its work.
You can never have a shorter chain overwrite a longer chain as the wallets will ignore any blocks not near equal in height with the current blockchain.
You could mine the rest of the blocks with less difficulty and catch up really fast.