Actually the deer came at high speed from the left and the car picked it up perfectly. In the dark running fast from left to right it was impossible to see. If it had been in front it would not have been an issue for me at all. Has nothing to do with inattentive - it was an additional safety net and worked perfectly. There are many ways to help an attentive driver. Accidents happen very quickly and the driver has little to do with them sometimes. 
There are many examples of Tesla’s not proceeding into intersections where cross traffic is not slowing down by mistake. 
It can also detect people about to rear-end you. If it can’t move forward it will beep and warn you of the possible impact. The autopilot system is always active in the background and able to help out in a split second if needed. If constantly benefits from over the air updates which improve the system with the latest FSD learnings. All without paying for FSD.