Why can't I delete music from my iPhone via iTunes?

"Back in the day" it was simple; I could go to "Music on my iPhone", highlight the songs I no longer wanted on my iPhone, press the 'Delete' key on my keyboard and voila! That song would "magically" no longer be on my iPhone.

Well, since this most recent batch of updates (complete overhaul of the Music app, incorporating Apple Music) I can no longer utilize this simple, easy, USEFUL method for controlling the content on my iPhone.

For those of you wondering, yes; my iTunes and iPhone are currently up-to-date:

And while I used to have "Manually Manage my Music and Videos" check box checked, it is now labeled "Manually Manage Videos":

Furthermore, there doesn't seem to be a way to remove any songs from my iPhone 6 without doing so one-by-one from my iPhone which is, let's call it "ridiculous".

Does anyone have any advice or perhaps some information that is glaringly obvious that I am simply overlooking?