Growing up in the Midwest, I remember being taught (not sure if this was official or something I got from my father, older brother, or maybe an uncle) to quickly assess if I believed that I would hit the deer or not.
If I was going to hit the deer, regardless of my actions, I was to accelerate into it.
If I could brake and avoid it, I was to brake.
I've been in that situation a few times. In the case of a collision with a deer, I accelerated into it and only took damage to the front passenger side panel. I do believe that it helped prevent a bad situation from becoming worse.
In the other cases, I was able to avoid a collision by braking.
Later in life, I did swerve once to avoid a large animal that I mistook for a person walking on a very dark, very rural road. My car flipped and slid on it's top ~100 ft. before coming to a stop. Myself and all 3 passengers walked away without incident but I still feel fortunate that we all did these many years later. Swerving is almost always the wrong answer.