Because Slytherin is the House you're Sorted into when you desire power, and - other than Lily - that's what Snape wanted the most. At the age of eleven there's no reason to believe he didn't have the same need to be powerful, and the same desire to be feared or respected, that he displayed a few years later as a teenager at Hogwarts when he began hanging out with future Death Eaters.
He may have also already developed his fascination with the Dark Arts even before he was old enough to attend Hogwarts, but even if he didn't, the neglect - and possible outright abuse - from his parents that would make him feel powerless, and therefore desire power so much, would have already happened.
It's not uncommon for children to travel to Hogwarts knowing at least a small amount about the four Houses, and to have made a decision about which House they'd like to be in, or at least which House they don't want to be in. The general reputation that Slytherin has which makes most kids say they don't want to be Sorted into it would definitely appeal to an eleven-year-old Snape.