On a multi-user system (linux), I created a private key with no passphrase. I can now encrypt a file and decrypt it locally without supplyng a passphrase. This is very convenient and appears to be safe. The encrypted file has read/write permissions only for the owner of the file (me). However I am interested in what risks I am open to by not protecting my private key with a passphrase, or how could another user on the system gain access to my encrypted file? I am not intending to exchange encrypted files with other correspondents, I only want to encrypt and decrypt my own files locally.
If they get a copy of your private key then they can decrypt files intended for you (files others encrypted with your public key).
So if they crack into your system somehow and get your private key, then you lose the security.
That's the reason for a passphrase, so even if they get the private key file they can't use it because they don't have the passphrase.