Why did Alex get rid of the map?

Alex (Chris) believed that by getting rid of the map he was being an explorer..... he wanted to discover something, find something previously unknown. Because this was actually impossible, he threw the map away..... and leaving himself in what became the unchartered territory he desired.

In coming to Alaska, McCandless yearned to wander uncharted country, to find a blank spot on the map. In 1992, however, there were no more blank spots on the map—not in Alaska, not anywhere. But Chris, with his idiosyncratic logic, came up with an elegant solution to this dilemma: He simply got rid of the map. In his own mind, if nowhere else, the terra would thereby remain incognita.