Because one of the lines’ arrows is facing in while one of them is face out, your brain automatically extends the line in the middle to make it look longer, (the arrow facing in,) even though both lines are the same length. According to psychologist Richard Gregory, this illusion occurs because of a misapplication of size scaling. In most cases, size constancy allows us to perceive objects in a stable way by using distance as a factor. In the 3D world, this allows us to determine a tall person as tall whether they are standing next to us or off in the distance. But, when we apply this to 2D objects, the human brain can make errors.
"Muller-Lyer Illusion." Optics For Kids. N.p., 2015. Web. 16 Mar. 2015.
Cherry, Kendra. "The Müller-Lyer Illusion - How It Works." About Education. N.p., n.d. Web. 17 Mar. 2015