In response to the question:
“Why is it easier to back into a space?”
A very good explination is given in a book called “The chicken from Minsk”. Unfortunately in seems to be out of print. A lot of people here would enjoy the book, I’m sure.
One of the primary points is that a line drawn through the axis of rotation of each tire points to the ceter of rotation for the car. In the case of the back wheels, the rear axis points at the center of the car’s rotation. In the case of the front tires each tire, individually, points to the center of the car’s rotation. Manufacturers have complicated systems to allow this to happen. (And they are not 100% perfect).
I don’t exactly remember the rest, but the basic idea is to focus on the rear axil, which is fixed, and always points to the center of rotation. If you reverse the car the rear axis will travel around the circle of the car’s rotation, alway pointing at the center, until the rear tire hits the curb. If you go forward, the rear axis will complete less of a circle, before the front tires hits the curb. So going backwards allows the rear axil to shift farther from the perpendicular with the curb, than if you pull forward. This means that the “S” shaped parking manuver can be accoplished in a shorter distance in reverse.