Instagram is a media company. They're only just now reaching a size where their audience is big enough for advertisers to care.
It's not just Internet companies that do this - practically all media start out in the red and don't make money for at least a couple of years. CNN, as an old media example, basically gave away advertising for its first several years of existence.
But that's not what happened here. Instagram, to my knowledge, has never made a penny off of advertising. There is no clear business model. Maybe it's advertising. Maybe it's charging for additional filters. Nobody really knows, not the Instagram founders and not Facebook executives.
How does anybody know whether a business would pay for advertising on a photo sharing app? People are always talking about "just turning on the profit spigot" whenever you want. I don't see any evidence that it is that easy.
It's not just Internet companies that do this - practically all media start out in the red and don't make money for at least a couple of years. CNN, as an old media example, basically gave away advertising for its first several years of existence.