yeah, like you always have time. You may THINK you have your 3000# vehicle under control, but you don't
my aunt one time sweved to miss a dog.... she lost control and stuck the car in a ditch (about 3 feet deep) She did this with my (then) 2 y.o. cousin strapped in a car seat and the 4 y.o. cousin seatbelted in.
I was about 12 y.o., but I remember my uncle went APESHIT ON HER (after he determined everyone was ok) Minor damage to the car but he went nuts saying "you risked BOTH YOUR KID'S safety to save a MOTHER FUC*** DOG?!?!?!?!" I remember it clear as day.... My aunt started hem-hawing some inconsequential excuse just to try and save some face, but eventually realized my uncle was right.
I had an old band director from highschool die in a few years ago over the same thing. Coming home from a gig he would do during summer times, he was on a long road in the rural part of town (notorious for deer). A deer jumped out and he swerved left onto the shoulder of the road.... he then overcorrected and rolled the truck 6 times, partially ejecting him and rolling with him hanging halfway out the window. Killed him. Ironically, he also still hit the deer and it had to be put down.
I bet he thought he had it under control right up until the point that he rolled it. Vehicles are designed to protect you from head on, even directly from the side. They are not so effective protecting you during rolls