Environment
Mac OS X Version 10.11.3 (15D21) Xcode Version 7.2 (7C68) Simulator Version 9.2 (SimulatorApp-643) react-native-cli 0.1.10 node v5.5
For me, my problem was that Mcafee is running on port 8081, so I run the app on a different port following this answer https://stackoverflow.com/a/50649969/5323419 Basically:
react-native run-ios --port 1234 react-native start --port 1234
I am using React native 0.55+