I use FaceTime on a daily basis and have always hated it wouldn't let me save calls to my Mac in the form of a media file. Surely Apple could have implemented such a feature if they wanted, but they didn't and I think privacy is a big part of that.
If for whatever reason you need to record FaceTime calls to a Mac, Call Recorder by Ken and Glen Aspeslagh, twin brothers from Massachusetts, has you covered.
The app creates a QuickTime movie file containing an audio track for audio-only calls and a video track for FaceTime video calls. QuickTime is an industry-standard multimedia container, meaning you can play your saved video and audio chats pretty much anywhere, convert the files to other formats in software like iMovie or Adobe After Effects, upload them to YouTube and more.