That's a completely non-related analogy. A better one is if you were to go to a university, become a student, use their facilities, and do research there, then

That's a completely non-related analogy. A better one is if you were to go to a university, become a student, use their facilities, and do research there, then the uni rightfully owns a percentage of any IP you come up with there. It's in their ToS when you signed up and that's what you have chosen to stick to. It's no different if you use FB or Instagram; you've agreed to their ToS that data you've pushed through their service is their's to do what they want with. If you're not happy with that, move along and use something else- perhaps print your photos onto your hypothetical paper and share them using that.