Here’s my simple take on the issue.
Leftists tend to espouse liberty in personal matters but are happy to endorse and encourage legal control of the economy; Rightists tend to espouse liberty in economics matters but look to the state to enforce moral codes. Leftists and Rightists compete with each other for control of the levers of power. Libertarians espouse liberty across the board as a result of which, their concerns cut across the left-right divide at right angles.
Of course, the reality is more complex than this and leftists will differ among themselves as will rightists but the broad picture is, I think, correct.