It's great that you bring it up, we had missed this one. I think it's better to say that the rule for questions is that the verb must come before the subject. After all, if there's no question word, the verb will be the first word in a question. Also, I've written some more about word order here: https://www.duolingo.com/comment/8970470
Never mind the he or she, but the order is actually important! The default order is "Varför ringer hon mig inte?".
If you wonder why she is not calling you, then you can change the sentence to "Varför ringer inte hon mig?" (like "all the others are calling me, but why isn't she").
If you wonder why she is not calling you, then you can change the sentence to "Varför ringer hon inte mig?" ( like "she calls everyone else, but why is she not calling me as well").
For sub-clauses, it works differently, but let's skip that for now :).