what's the actual way to see who doesn't follow you back on instagram?

Heads up that the download isn't instant. It gets prepared in the background and you get a notification when it's ready, could be minutes, could be a day for a big account. Pick HTML if you just want to read through it, JSON if you're going to do the spreadsheet thing.

There isn't a button for it. Two honest options. Small account: open your Following list and use the search box on it against your Followers list. Tedious but fine for a couple hundred. Bigger account: Accounts Center > Your information and permissions > Download your information, pick just Followers and following. You get two files and can compare them in a spreadsheet. Skip the "unfollowers" apps that want your Instagram password. That's how accounts get hijacked or flagged.