Why solo backpacking? To be honest, one of the reasons I sometimes go alone is simply that it’s tough to find people to go with, especially on short-notice. So reason number one is just the sheer necessity. But that is not the only reason to enter the wilderness by yourself.
Another reason to backpack alone is related to the first: simplicity. For example, if you like to go light, you may have conflicts with friends who want to share the weight of heavy cooking gear and tents. You may prefer cheaper trips, rather than joining others on a flight to some distant locale that isn’t any more beautiful than the trails within hours of you. In other words, you might not want to trade three affordable adventures for one expensive one.
Going solo gives you freedom as well. Even the best hiking partners will not need breaks at the same time, get hungry at the same time, want to hike the same distance each day or do the exact same things. When you’re alone in the wilderness, there is a natural rhythm that can never be there when several people’s needs have to be taken into account, and you are free to follow that rhythm.