Ctrl+a Was Already Taken

One socket, two plugs reaching for it
One socket, two plugs reaching for it

Some people change the tmux prefix from Ctrl+b to Ctrl+a in their config. Why Ctrl+a?

Because that is what the fingers learned on GNU Screen, whose prefix is Ctrl+a. In a shell, though, Ctrl+a means beginning of line. The prefix takes it, so on Screen you press Ctrl+a and then a to send the real one through to the shell.

tmux's Ctrl+b was not free either. In a shell it moves back one character, and the arrow keys cover that. In tmux, pressing Ctrl+b twice is how you take that stolen key back.

Whichever key you pick, something is taken. Choosing is deciding what you can take back.