If a hash is calculated on the client, the client authenticates to the server by submitting their hash. The server then compares the hash to the database entry. This means that *if the database is exposed, attackers can authenticate as anyone by submitting the correct hash. Even though they cannot determine the original passwords, they can still use the hashes directly to break authentication*. With client-side hashing, the hash effectively becomes the password.
UPDATE: btw, you still have to send it over SSL to send it securely and I suppose it's not a bad idea to also hash it client-side so that it's never transferred raw.
The question whether to hash on the client or the server presents a false dilemma: it’s possible to do both. By hashing on the server, passwords are adequately protected even in the case of a database leak. By hashing on the client, the password doesn’t leave the user’s browser and even the web application doesn’t learn the password.
However, client-side hashing protects against innocent mistakes. If the application doesn’t handle the password, it can’t accidentally mishandle the password.