Should I allow communication firewall on public vs private?

I am copying an answer from Microsoft Answers as it answered the question much clearer than I could explain regarding the firewall on public vs private. Private networks or home networks are when you know and trust the people and devices on the network. Computers on a home network can belong to a HomeGroup. Network discovery is turned on for home networks, which allows you to see other computers and devices on the network and allows other network users to see your computer.

Public networks are the networks in public places (such as coffee shops or airports). This location is designed to keep your computer from being visible to other computers around you and to help protect your computer from any malicious software from the Internet. HomeGroup is not available on public networks, and network discovery is turned off. You should also choose this option if you're connected directly to the Internet without using a router, or if you have a mobile broadband connection. I would like to inform you that system network configuration does not come configured with a network. You have to configure it when you connect to the Internet connection for the first time. When configuring the network connection to the system it might have got selected to the public network. However, you can change Public network to Home network from sharing center.

• Go to settings and click on Network & Internet.
  
• Click on Wi-Fi on the left pane, and click on the Manage known networks.
  
• Click on the wireless network connected you want to manage and click on Properties.
  
• Now turn on Make this PC discoverable.
  

A point missing about the public network option is that sharing services SMB, etc.. should be disabled and open ports will be greatly limited. Less open ports result in fewer attack vectors. So, choosing a public network when you are using an untrusted network is much wiser. Why is the default to allow public networks, and disallow private networks?  This is likely because most non-technical users will select the default option, which is likely safer.