I never had an issue with Apple Music. Once you understand there are two distinct sections for music, the catalog and your Library (and that you can add components of the streaming catalog into your library), it's pretty easy to use.
I think this separation is not what makes Apple Music so unintuitive. For me, the complexity lies in three things: the abundance of drill-down menus, the bloated ’New’ section (where Apple put everything that did not fit anywhere else) and in iTunes the mixed use of right-click menu and three-dots menu.
On iOS, you can drill down into menus
ad infinitum, because there are just no end points. You can go from Song > Artist > Songs > Artist > Albums > Artist > ... and so forth. You can lose track of your exact location really quickly. It is even worse when you throw a search into the mix, because the search results will just be put on top of that hierarchy. In iTunes, there are no horizontal navigation views with clear back buttons, but the entire views change whenever you click on something. You can only go back with this browser-like back button that may or may not take you back where you came from. It frequently threw me back to the beginning, not the last step. Sometimes when you want to see more songs from a particular artist, it throws you from My Music to a search page on New, where the back button will not work at all.
The ’New’ section is not really all about ’new’ stuff, it is basically everything that is not ‘For You’. If you scroll through that section, it does not make all that much sense. It is also a huge list to scroll through, with lots of sub-sections that you can check out. I almost never got to the bottom of that list. They should have used a segmented control at the top, like they use in the iTunes Store app. They could rename ‘New’ into ‘Discover’ and offer sections for ’New’, ’Top’ and ‘Activities’.
In iTunes, you can often choose between the standard right-click menu and the three-dots menu, but there are lots of places where you can only use the latter. In the ‘New’ section you cannot use the right-click menu at all. In those places where you can choose, the menus are not even consistent. Menu items are not in the same location and it seems as though you are always looking for the right button to click. It felt tedious after a while to constantly adjust to this silly three-dots menu when everything else on OS X uses a right-click menu.
Apple Music is just not the intuitiveness and focus that I have come to expect of Apple software. It feels like an attempt to put as much functionality into a small app. I’ve seen several WWDC developer sessions on UI design and to me Apple Music seems like an example of how to fail at basic design conventions.