Apple's rules are not hard to understand: they want a cut if an app is sold through the App Store, or if a subscription is sold through an app from the App Store. And as a necessary part of this, you can't advertise in your app, "hey, let's go around the corner and do a deal where Apple can't see". If their terms weren't across-the-board, if, say, they allowed in-app subscriptions without taking a cut, then before long most apps would switch to free-but-in-app-subscriptions, because, of course, developers like money - that's understandable. But if there's a way to not pay the App Store, then in practical terms the App Store will not get paid - some tiny loophole will become every developer's preferred avenue. And Apple's not going to run the App Store at a loss.
Amazon has a Kindle app for iOS - it's a great app, I have it on my home screen. It's only useful for reading books purchased from Amazon, which you can't buy in the app. Amazon doesn't seem to have a problem playing by the rules they agreed to, and they sell tons of books. They have attracted people to their business of selling ebooks, and to the Kindle "brand" - they've gotten the word out, and they're very successful.
Spotify wants a way to reach their subscribers to tell them to pay Spotify directly so Apple doesn't get any money out of the arrangement - understandable, because Spotify likes money (so much so that they pay the actual artists a pittance - if I understand correctly, Spotify is the streaming service that most artists like the least). And there are plenty of ways that Spotify can get the word out: they can advertise on the Internet, they can put ads in magazines and newspapers and on TV. But that would cost them money. And they like money, so, effectively, they'd much rather do the advertising for their service, for free, on Apple's dime. Now, if I came into your restaurant with signs and banners advertising my restaurant, how well do you think that would go over?
And they're lying about how this has played out. They're playing this as them being pushed around by Big Bad Apple, when Apple just wants them to play by the rules that they - like everyone else - accepted to get into the App Store. They paint themselves as the underdog here, when just a little while back they were crowing about how much bigger they are than Apple Music - you can't have it both ways. I don't have a lot of respect for Spotify at this point.