Deleting Pictures

If your Mac and your iPhone are connected through iCloud, then the are synchronized, meaning they will always have the same pictures. If you add or delete pictures on one device, the same will happen on the other. Of course, that's what synchronized means!

Why do you want them un-synchronized? If it's to save storage space, you can, in Mac Photos, go to Photos>Preferences>iCloud and check "Optimize Mac Storage." The devices will still have the same pictures, but the Mac will keep smaller versions to save space. The full image will still be available for editing and printing.

If you are embarrassed by a picture you can hide it:

Hide photos from view in Photos on Mac - Apple Support (BY)

OK--there are other reasons to hide pictures rather than just embarrassment

To disconnect your Mac and iPhone as far as Photos libraries are concerned, disable iCloud Photo Library in Photos on one or the other (or both if you have no other use for it).