You define conservative and liberal etymologically. The author defines conservative as seeking power limited to some and liberal as seeking (equal) power for all. Your definition and his definition are conflated in your characterization of the author’s views in writing "For to you a conservative only seeks to conserve bad things and liberal seek to enforce equality."

You also write “We are all born with equal rights as human beings.” Society grants you rights. Outside of society, strictly speaking, nobody has any rights—there is no one and no thing in the world to grant them to any effect.

You further write “Society, however that is defined, has no higher right than have I. It has no authority to compel anything of me.” However, you are in a social contract. In exchange for rights and benefits, you grant authority to society.

In principle, there is no good or bad in a social contract if the parties agree to it. As I remember William F. Buckley, Jr., and others putting it, the politico-philosophical dispute over how to implement them revolves around people’s views of the malleability of human nature. Liberals are optimistic about the good in people and pour on social programs liberally to perfect society. Conservatives are pessimistic about the bad in people and pursue social programs conservatively to prevent abuse and bad outcomes. Conservatives are associated with pre-democratic governance, because overturning power structures can lead to things like the Reign of Terror.