The estimates are for a "functional prototype", which is, the implementation of ONLY functional requirements. Non-functional requirements are not mentioned here

The estimates are for a "functional prototype", which is, the implementation of ONLY functional requirements. Non-functional requirements are not mentioned here, and in the case of Instagram, there are many. Then, since Instagram is a service, you need some sort of operations team to manage and monitor the infrastructure. You will also need some sort of testing (quality assurance, performance and scalability, security...). Then you will need some degree of organization to accomplish this. Additionally you will need some visibility and minimal critical mass of users to get the ball rolling (aka user acquisition). That is of course, not development, but this is one of the most expensive items, to the point that for some apps, development costs are marginal compared to user acquisition costs. You might get a software with the Instagram user-facing features, but don't expect to be able to handle the volume of traffic that Instagram does, at the level of security they do. That last part is actually a key aspect of the business model that I couldn't found anywhere in the article.