Hi Alexandra,
In this situation, it may be best to just come right out and ask him to hang out on a specific day.
He is very passive aggressive with you.
He may have conversations with you on Instagram, but he hasn’t initiated any of it.
He may like your pictures on Instagram, but he doesn’t follow that up with making conversation or flirting.
If you don’t make a truly aggressive move soon, you may end up being that online friend that he chats with from time to time and likes their pictures.
He seems to have some interest in you but it is fairly weak.
Asking him out directly may or may not ignite that interest and thereby compel him to become more aggressive with you.
However, doing so will at least give you an opportunity to either move this interaction forward romantically or have good reason to let it go.