Can I keep photos on iMac but remove them from iPhone 12 Pro?

Joanneeley wrote: We have a new iMac, and now everyone's photos for the past 20 years have appeared on my iphone 12 pro.… How do I remove them?

Don't delete them!

The only way I can think of that pictures could silently arrive on your phone is through iCloud. iCloud synchronizes Photos on different devices. If you have iCloud Photos turned on for your iMac, then all the pictures there are copied to Photos at iCloud.com. Then, if you have iCloud turned on at your iPhone, all the pictures from iCloud.com are copied there. If you delete pictures on your phone, then they will be deleted everywhere else that's connected. All Photos on connected devices are kept the same.

In each case of copying, it was "If you have iCloud Photos turned on…" So the solution would be to turn off iCloud Photos on any device you don't want connected. Once the device is disconnected from iCloud, you can delete pictures. I'd start with a few, wait a day, and check with iCloud.com and other devices. I'm always nervous about deleting things.

On an iPhone, you can switch iCloud Photos off at "Settings>Apple ID>iCloud>Photos" by switching off "Sync this iPhone."

On a Mac, go to Photos' Settings>iCloud and uncheck iCloud Photos.

Turning off and deleting local pictures will leave the pictures at iCloud.com.

There must be more to the story. Just adding a new Mac should not intermingle photos from various sources, even with Family Sharing if properly set up. Each person should have a separate Apple Account (previously called Apple ID) that the use on their own device(s). If several people use the iMac, each should have a separate Mac account and Photos library connected to their own Apple Account.

Joanneeley wrote:

... We have family sharing. No current photos appear.

Family Sharing is just sharing the iCloud Storage but not the contents. But it creates a Shared Family album. Could someone have added the old photos to this album? Only the person who shared the photos can remove them again from the Shared Family album.

Or are you now using a Shared iCloud Photos Library? In the Shared iCloud Photos Library you can delete each others photos. The person who added the photos to the shared library needs to remove the photos that theaters do not want to have on their devices.

Joanneeley wrote: … If I re-connect the iClouds I wondered if they will re-download.

Since iCloud synchronizes Photos Libraries, then when you connect Photos to iCloud, it uploads and downloads everything so they will be the same.

My use of Shared Albums and Shared Libraries is very limited. léonie is much more experienced, so her advice is very trustworthy.

If you had "Optimize Storage" turned on in the iMac, then you don't have the full images on your computer's internal drive-- you have smaller files. That's why, I think, the Mac is telling you that there's no point in saving the smaller images.

If you have more pictures than will fit on your computer, then your only solution is to get an external hard drive. That's a good investment in any case. You can create a new Library on the external drive, make it the System Library, and connect it to iCloud with "Keep Originals." Then wait, maybe weeks, for that Library to fill up with all the pictures. When you know that they are all safe, you can disconnect from iCloud.