Oh that's not alarming at all. But I can totally fix it. No wait, I can't!
Well now I'm stuck. I can't continue syncing, but there's not really a graceful backing out option either. I'm an optimist, so I clicked “more information.” Now, Apple has a nice page about deauthorizing extraneous Macs. It's all nicely formatted with links to other parts of the page and such, but it lies. Clearly Apple spends as much time in iTunes 12 as everyone else does (which is to say, as little as possible) so this page only shows how to do this if you aren't signed in. I was already signed in so this was useless to me. Now I can't get my iPhone to sync, and as an added bonus Apple's own help page won't tell me how to fix it.
This is where I would put a mention of how my fondest wish is that Tim Cook walks on stage at WWDC 2015 holding iTunes 12 source code and feeds it to a woodchipper. You know, if I held a grudge.
Here's how to do it:
First, go to iTunes and if you're not signed in, click on Store > Sign In. Then click on your name in the top right corner, and choose Account Info:
Click on Account Info in the menu with your name on it.
Now that you're in the account info, it's a piece of cake to find the deauthorize button:
At least it's a big obvious button when you end up in the right place.
So click that, and after the requisite “no, really, do you mean it?” dialog boxes you can start over with your authorizations. Note that this is on a yearly timer, so you can't do this once a week or anything.
There are a few other useful items in here too. You can change which Apple ID you use, your payment card and billing info, iTunes Match, and even review any hidden purchases.
The account info “below the fold” in iTunes.
Some of this information is also available at My Apple ID, but if you're already digging in to iTunes anyway, it's convenient to have all of this available in one place. Now if only Apple were better about telling you how to get there.