The term right, left, and centre are based on the seating arrangements of the French parliament which, in the 18th and 19th Centuries, was shaped like a horse shoe with the speaker placed at one end. Seating was divided among three major sectors, right, left, and centre.
The right side or wing (on the speaker’s right) was occupied by groups of various kinds of conservatives, the centre by liberals, and the left by socialists in several groupings. Each group was subdivided and the more radical moved to the extreme right (reactionaries) and to the extreme left (communists).
Each term is identified by a philosophy or ideology.
The right is conservative, people who believe that humans are more bad than good, need super wise men to lead them, people who see a relationship between the church and the state to tell the people what is right or wrong, much attracted to tradition and history, suspicious of democracy, favouring free markets and free competition.
The liberals, for whom John Stuart Mill is a spokesman, believe that people are naturally good, rational, and able to govern themselves. There is a need for government, but limited government. Liberals do not fear change, have no great attachment to tradition or history, and believe the church and state should be separated. Liberty is their prime value: class structure is not thought important. Most liberals like the free market and they value private property.
The socialists dislike the free market because it leads to monopolies and abuses, exploiting the workers. Power should be centralized, more industries should be owned and run by the state and there should be central planning on a wide scale. Extreme socialists, unlike socialists “on the right,” likely see violence as a legitimate and necessary means to bring about political change.
Personally, I think they all miss the boat. Set something up to support apprenticeships, the independent small business person, innovators, and have profit sharing, day care, and school rooms for the worker’s children in the larger corporations. Come up with a system that supports this. Then we’ll talk.