I understand the word "anarchy" to mean "without a political leader" rather than "no rules". Consequently, it would seem that "anarchy" has roots in "an-" and "hierarchy". Is this correct, and would someone provide more detail?
Medieval Latin anarchia, from Greek, from anarchos having no ruler, from an- + archos ruler First Known Use: 1539
Technically, you are correct, but it is the implications that are important. If there is "rule by no-one", then there are, by definition, no rules, because there is no-one to make any rules. If I refuse to accept that anyone has a right to impose any rules on me, I am free to do what I like, and what I want.
As with other similar words, the precise meaning has been expanded to include the implications of the meaning, which is reasonable, as it them becomes a shortcut for "the results of an anarchic system".
Consider, as a similar case, the word "democracy", which technically means the rule of the people, but has been expanded to mean the election of rulers by all of the people. It is a different thing, but it is the outworking of a practical system of democracy*
*possibly. That is a discussion for somewhere else.