Deer on the road is an edge case that humans cannot handle well. In general every option other than hitting the deer is overall worse - which is why most insurance companies won't increase your rates if you hit a deer and file a claim for repairs.

The only way to not hit/kill hundreds of deer (thousands? I don't know the number) every year is to reduce rural speed limits to unreasonably slow speeds. Deer jump out of dark places right in front of cars all the time - the only option to avoid it that might work is either drive in the other lanes (which sometimes means into an oncoming car), or into the ditch (you have no clue what might be there - if you are lucky the car just rolls, but there could be large rocks or strong fence posts and the car stops instantly. Note that this all happens fast, you can't think you only get to react. Drivers in rural areas are taught to hit the brakes and maintain their lane.