can't delete photos from mac

Have a look at Photos Help (choose Help from within the Photos App), search for "delete." Deleting images is more complicated than it used to be, note that in some instances COMMAND-Delete is what you need, not just the Delete key:

Delete photos and videos

1. In the Photos app on your Mac, select the items you want to delete.
2. Do one of the following:

• • Delete selected photos and videos in Days view: Press Delete, then click Delete. The selected items are deleted from your library and placed in the Recently Deleted album.
  • Delete photos and videos from an album, but not from your library: Press Delete. The selected items are deleted from the album only and remain your library.
  • Delete photos and videos from a Smart Album (for example, Last Import, Favorites, or Videos): Press Command-Delete. The selected items are deleted from your library and placed in the Recently Deleted album.
  • Delete photos and videos and then permanently remove them from the Recently Deleted album: Press Command-Delete, then open the Recently Deleted album. Select the items you want to delete permanently, click Delete, then click OK.

If your Library is not behaving as it should, make a safe copy of it and then try to repair the original as described here:

https://support.apple.com/en-us/HT204967

Are you trying to delete them from an album view, or the all photos view?

Deleting from an album view normally only removes them from the album.

Where is your library stored? On the system drive, or an external drive?

If you click on the library, and open the info pane (CMD-I) what does it shown in the permissions section at the bottom?