Words like “employee,” “payee,” and “detainee” support the generalization, crudely stated, that words with the ending -ee designate the person affected in the specified way by an action performed by someone else.
Summary
It doesn't make a ton of sense to worry about the "argument" here, since the question is very specifically about picking a word that would function in the same way that "absentee" did.
The author started by proposing a general rule:
If it ends in "-ee", then it designates the person affected by someone else.
An employee is employed by someone. A payee is paid by someone. A detainee is detained by someone.
But then the author thinks of an exception: absentee.
An absentee isn't absenteed by someone.
Goal
So we need to find a word that has the same problem as absentee had. It doesn't end up referring to an action that someone else did to you.