If you are trying to stream to Twitch (or another service) using Elgato Game Capture HD for macOS, and the Live Streaming button is greyed out, the following steps may resolve that problem.
Please Note: These steps will erase your Elgato Game Capture HD preferences, which means you'll have to re-adjust your Settings and Preferences back to the way you prefer.
1) Go to the Finder by clicking on the Desktop.
2) In the Go menu, select Go To Folder...
3) Type the following: ~/Library/Preferences
4) Press the Go button.
5) Find the com.elgato.GameCaptureHD.plist file and move it to the Trash.
6) Restart your computer.