Why can't I allow connections for Control Center in Firewall settings?

That’s the only thing the Application Firewall blocks, what you want to do.

A firewall is a network management tool that blocks access to devices and services. If you thought it was a security tool, you were misinformed. Turn it off and use your Mac to get things done. Are there users and devices lurking inside your LAN that you think are threats? The Application firewall only blocks things inside your LAN.

VeryTiredofApple wrote:

I can't get airplay to work on my Mac without disabling the firewall. With the firewall off, airplay works seamlessly, but if it's on, I get the "AirPlay Unable to connect" error on my iPad. I suspect that the issue might be with the firewall setting for the Control Center.app but the system won't disable it. I can toggle the setting for all the other firewall items on and off, but for Control Center, it constantly reverts to blocked so I can't test it with it set to "allow incoming connections". Others seem to have the opposite problem.

Is anyone else experiencing this? Any idea as to what's going on?

I would not turn on the application Firewall.