The numbers don't quite add up, however. For one, the backlash against Instagram — the real heat of the moment, such as there was one — peaked on Dec. 17 and Dec. 18. This drop came on the 24th, when the controversy had cooled. In addition, AppData's numbers measure Instagram use through the Facebook app, which is vulnerable to outside factors. On the 20th, for example, Facebook announced a revamp of its privacy tools — including tools for limiting how apps are installed and share — for all users. That, more than a user exodus, could account for such a large drop. Facebook's app user reporting is also somewhat inconsistent.
By contrast, look at the AppData numbers for Flickr:
There's a much better case for an Instagram exodus, albeit a much smaller one, to be found here: The numbers spiked within a couple days of the backlash, plateaued, and started to settle back down. This is very likely the trail left by disenfranchised Instagrammers.
Furthermore, there is reason to believe people left Instagram for real. Not many, and not on the 24th but on the 18th.
For the first time since we've been tracking it, BuzzFeed's Instagram account, which has over 13,000 followers, posted a loss in the 18th. The loss was small, at just nine people. But a typical day in the last two months has seen the account gain about 45 followers. Assuming people were joining at about the same rate as before, and that our drop came from people leaving, that means about 55 people — nearly 0.5% of our followers — closed their accounts. Update: The Times' Nick Bilton tells BuzzFeed FWD: "A month ago I was hovering near 230k users, now I'm a stones-throw from 225k." This timeframe includes not just the TOS controversy, but the removal of Twitter cards from Instagram.
If this represents a trend across Instagram, the service will have lost about 500,000 of its 100 million users (though most would have been replaced by new users). This scale seems plausible in the context of the 50K spike in Flickr users on Facebook.
It's not much, and it's certainly not the nearly 25% that is being claimed elsewhere. But it's something! Instagram is a service that grows on most days. And for at least one, at the height of a media controversy, it appears to have shrunk.
Update: Instagram has officially denied the 25% loss claim, but offered no specific numbers.