Hey there,
So I do not know the exact specs of your particular machine but looking at a few versions of the Macbook Pro 2013. It should be fine hardware wise. The OS is fine for the game so whatever is causing the freezing is likely related to some sort of software conflict with other programs on the system or perhaps a network/connection issue. I have some troubleshooting you can try that should help clean things up.
First, if you are using an external monitor, try disconnecting that and playing on the integrated monitor for the Macbook, see if the issue persists.
Try doing a power cycle on your system. Turn off all devices including the modem. Wait 60 seconds, turn on the modem, wait 5 minutes, turn on any network devices, wait 2 minutes, turn on your computer and try the game.
You can try switching your DNS settings to use a free public DNS servers instead of your ISPs Servers:
We do not have individual steps for specific modems or routers so if you need assistance accessing or updating the devices, contact the device maker/provider.
Perform the steps listed on this article to remove the Blizzard Desktop Application from the system: Blizzard Support - Uninstalling the Battle.net Desktop App
Try running your system in selective startup mode: https://battle.net/support/article/200483
Our clients do not support installation on encrypted drives using programs such as File Vault. There can be issues installing, updating, launching or connection issues due to the encryption. If drive encryption has been enabled, please disable it and allow the drive to decrypt: Blizzard Support - Checking for FileVault
Create a new administrator account: Blizzard Support - Creating a New Administrator Account
Once the account is created, shut down the computer, wait 60 seconds, restart, log into the new profile and try the app/client.
I hope that helps you out and gets you back to playing normally.