argilo

There is no -il- in this word, and you should say so out loud once. Esperanto's -il- is the tool suffix, and it is so productive that learners start seeing it everywhere: tranĉilo is a cutting tool from tranĉi, ŝlosilo a locking tool from ŝlosi, kudrilo a sewing tool from kudri. So argilo looks like a tool for doing something called argi. It is not. There is no root arg-, argi is not a word, and argilo is a single borrowed root that happens to end in the same three letters.

This is a whole class of trap, not a one-off. Fusilo, a rifle, is not a tool for fusi. Vetero is not vet- plus -ero. Ĉevalo is not a valo of any kind. The suffixes are real and productive, which is precisely why a coincidence with a borrowed root is so easy to misread: the machinery works often enough that you stop checking. The check is simple. Take the supposed base away and ask whether what is left is a word. Arg- is not.

A clay is not a tool anyway, which is the semantic tell before you get anywhere near the dictionary. -Il- makes instruments: things you hold and use on something else. Argilo is a material, in the same family as ŝtono, sablo and ligno. If the word had been built rather than borrowed it would have been an -aĵ- word, not an -il- one.