There are a lot of times when a pilot may not be "sick" but is still not fit to fly. We have that one dork, loser of an ACP who has been called the sick Nazi because he is so hard over on guys not using sick time unless they are what he considers sick. (Not sure if he's still an ACP or not)
If your kids are sick, your parents are ill, your wife is injured etc., you may not be fit to fly.
I would like to see the language changed to "personal time".