Hello! I noticed that this had been a problem in the past. I am using the Xbox One Elite controller. It works fine on other games, however when I play Halo MCC or Halo 5, when I turn/look right, it moves at a very slow pace. Looking left works fine. I thought it was my controller at first, but when I play other games like Rainbow Six Siege and Battlefield, it works as it should. Thanks!
Check in your sensitivity settings when you are in the Halo lobby. They might be set too low.