One clear reason to run the proxy is that it allows you to securely connect to your Cloud SQL instances with MySQL Workbench. You can get the IP (hostname) and port from GCP no problem, but to connect, you need to be running Google's proxy. (You also need to create a JSON credential file from GCP and add your IP to the Authorized Networks BTW.)
The reason for the error is that both the proxy and the local default install of MySQL will try to communicate on port 3306. When you try to start the proxy, this is the result:
doom:project cawood$ ./cloud_sql_proxy -instances=instancename-9999:us-west1:instance=tcp:3306 -credential_file=CredFileName-dflkjal.json &
2017/06/05 23:51:24 listen tcp 127.0.0.1:3306: bind: address already in use
To resolve this error, one solution is to create a config file for the local MySQL server and change the port.
One thing to note (as per the MySQL documentation) is that the installer for macOS will not create a config file: "Note As of MySQL 5.7.18, my-default.cnf is no longer included in or installed by distribution packages." If you don't have a config file already... to create the config file, simply run these commands.
$ cd /etc
$ sudo nano my.cnf
[client]
port = 3366
[mysqld]
port = 3366
It's worth noting, that I used to see this error before I installed MySQL locally. The reason was that there was another Cloud SQL Proxy process ("cloud_sql_proxy") already running. The solution to that is simply to kill the process.