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Why "administrator" instead of "administer"?
The common joke is that English is actually a dozen different languages hiding within a single trenchcoat. Just because some words and groups of words look similar and are spelled almost the same doesn't mean they follow the same linguistic rules because they might've come from a completely different language using a completely different linguistic system or a completely different time period. It's really almost impossible to tell how to work with a particular English word without knowing its backstory, even when there are "rules", most of the rules have plenty of exceptions because of this.
Trying to draw clear, consistent, universal patterns out of the English language is a fool's errand. If you wanted to achieve that, you'd need another language. (and then English would probably steal a bunch of its words too)