I recently graduated with a degree in Mathematics - I'm still proud - which clearly means I can't string a sentence together, let alone spell. It also means I like simple rules.
According to the Oxford [English] Dictionary, English has a simple rule:
The ... rule [is] that the final silent e [of a word] is kept when adding endings that begin with a consonant.
But argument ignores that rule; how rude!
TIME World recently published an article about misspelling. Ken Smith, a senior lecturer in criminology at Bucks New University, is so fed up with correcting freshers' spelling that he believes that we should start accepting minor variant spelling, rather than just marking them as wrong. So, I will be using the variant spelling of arguement from now on.