It's worth remembering that while every design/dev decision impacts the user experience, not every decision can be rationalized from a UX perspective.
There's no easily-findable explanation by the creators of Instagram of why there's no zooming.
Constraints and the Creative Process
This is speculation, but it's based in logic. Instagram is a tool that utilizes constraint as a way of influencing the process of creating content.
- There's no convenient way of uploading from the desktop, so you've got to use a mobile device.
- There's only one crop option. A 1:1 square crop.
It's arguable that not allowing users to zoom is another such constraint. It encourages those uses who care enough about the result, to capture images that work in that aspect ratio and in those dimensions. To create images that don't need to be zoomed.
Of course, it's likely that the real reason is something like they forgot to include or enable the feature, and then post-rationalized the constraint argument as a reason to not change things.