In version 1.2.5 and earlier, your screen would tilt towards the direction you took damage from, acting as a bit of a directional damage indicator.  As of 1.3, due to the change made where single player games now run as an internal server, the client and server are de-synced, the server no longer sending the angle of attack to the client, and therefore the client defaults to tilting only sideways to the left whenever you take damage now.

The code for this to work is still in the game today, unchanged for 8 years since 1.2.5, and can be quite easily fixed, as I made a video showing this off in far more depth and explanation, and we (Charles and I) actually managed to fix this as a Forge mod with relative ease for most later versions of Minecraft, including 1.16.3.

Here is the video in question:  https://youtu.be/pAJPc71YOnY