Many calendar apps include an "internal" or "device only" calendar as well as allowing sync. Just looking on my own phone I can see that aCalendar+, Business Calendar 2 and Digical all offer local or unsynched calendars. Google's Calendar app doesn't seem to, but that's no surprise: Google don't want you to be keeping information out of thei systems. It might be that your calendar app supports such things too but you've not created a local calendar within it, so I'd check the settings. Otherwise there are plenty of calendar apps out there, and most will do what you want (and if you turn off any online calendar accounts in their settings and set the local calendar as the default then you'll never need to worry about the fact that they can also sync if wanted).
I might add though that your calendar app's behaviour is odd, since even Google's Calendar app allows me to add events when in airplane mode: "sync" means "sync when online", not "you need to be online to do anything". That may be because you've not created a calendar account in it yet?
There are offline-only unsynced apps, but as I do want sync (e.g. I want many of the event calendars from my different collaborations to stay updated on my phone) they aren't useful to me, and so I can't name any for you (I see an interesting app, realise it cannot sync at all, never read any further).
