You encrypt an e-mail so that if it is intercepted it can't be read. If you send them the key, and it is intercepted, then the mail can be read (unless you encrypt the key, and then....).
Private/Public key encryption is very clever in that even if someone else has the recipients Public key they can't decrypt the message; they need the Private key to do that. So you can encrypt the message using only the Public key, but to decrypt it you need both keys; clever.