Unable to delete songs from my iTunes Library

I have a sizeable library of music in iTunes on my MacBook Pro and I'm trying to trim it down. I find that I cannot delete songs/tracks easily anymore. I used to be able to press the "delete" key and they would be deleted from the Library. The only way I appear to be able to delete songs is to delete an entire album.

This problem is new. For background: I am (and have been for many years) a subscriber to iTunes Match, and about a year ago became a subscriber to Apple Music as well (yes, I have both operating simultaneously).

Is there any way to delete songs easily? Example: I have an album where I want to delete most of the songs and leave a few. It is an album that I uploaded manually into my iTunes Library years ago. I can't select a group of songs and delete them. I press the "delete" key and just get the "cannot do this" sound.

Many thanks.

[Re-Titled by Moderator]