With all the crazyness about Instagram and how they own your pictures (not mine, I never used the service) it raises the question as to why Twitter is letting us export our tweets now? You don't see how they're connected? Read on...
Instagram's answer for those people who don't like it is this -- opt-out. You can download all your content, close your account, and we won't own anything. They're banking on the assumption that most people aren't paying attention, don't understand, or don't care if they use their picture of their beloved Aunt Amy to advertise a brand of cookies that caused her demise. There are some truly bizarre possibilities.
So maybe Twitter wants to use our pictures that way too -- esp since they now have access to all the pictures we post from other services, the ones who support the Twitter Cards API. Which of course until last week included (tah dahh) Instagram.
The order in which things come public isn't necessarily the order they became known to the companies pulling the strings. It's quite possible Instagram gave Twitter a heads-up about the licensing change, and that Twitter told them to cut the cord, before dragging them into the mess. Or whatever. You just can't know what they're telling each other behind the scenes.
So back to the question raised in the title.
Maybe Twitter is letting us export because something bad is coming that they want to be able to offer an export-to-opt-out feature like the one Instagram is offering. A change in TOS that will be so unpalatable that if there was no way out, the FTC would stop the change (and rightly so).
Maybe it's just Twitter being good guys. Wanting us to feel good about them, and maybe even wanting to enable new applications, which the JSON-based archive certainly does. Unless of course there are onerous licensing terms lurking in here somewhere. ;-)
One more thing. To publishers who act as if Twitter, Facebook, etc are part of the open Internet, maybe now you're getting the idea that this is not true. These are corporations who think and act just like you do. They are very likely future competitors of yours. And if you don't think of them that way, at least as a possibility, you stand to lose, big.