how do I prevent photos i delete on my phone from being delected on my mac?

If you use iCloud to synchronize Photos on your Mac and iPhone, then you will always have exactly the same pictures in iCloud, on your iPhone and in your System Library that is connected to iCloud. That's synchronization!

But there are a couple of things to keep in mind. One thing is -- having the same pictures doesn't mean they take up the same space. If, on your iPhone, you go to Settings>Photos and turn on "Optimize iPhone Storage," then the pictures on your iPhone will be smaller and take up less space, but they will look the same on the phone, they'll be available in full size when you want, and you can edit and use them just the same as always. You can do the same in Photos>Settings on the Mac to save storage space, there, too.

The second thing is the "in your System Library that is connected to iCloud" part. You can have more than one Library on a Mac, but you can have only one System Library, and only the System Library can be synchronized by iCloud. So, you could create a new Library on you Mac (close Photos and Option-Click the Photos app icon), and put pictures in the new Library that you don't want on your phone. Then you can delete those from the System Library-- they'll still be in your new Library, but they will disappear from you phone. Always Have a Backup! On the Mac, you can switch back and forth between libraries with that option-click thing. The phone must shows the System Library pictures.

I have several libraries, and my System/iCloud Library has only my favorite Photos that I want to look at or to show to friends. Works great.

So, you can Optimize Storage and have a Favorites Library to save lots of space.