It think it's more that, like with everything to do with Politics, the words have been repeatedly redefined by people who wanted to obtain the support of pre-existing tribalists emotionally bound to one or the other as "tribe" markers, and what is now said to be Left and Right is the product of a lot of such manipulation.

As I see it there is definitelly a range between the pure selfish "I do what's best for me and fuck everybody else" thinking and acting and the entirelly selfless "think of everybody else" one and somewhere in between sits a vague border one side of which can be thought of "left" and the other "right".