Terminate Messages from iPhone appearing on Macbook Air, it's an annoying, irritating distraction

Can someone please help me STOP my phone from sharing its activity with my MacBook? For me, it's an irritating distraction and I DO NOT want it happening. I don't need the MacBook mirroring my activity on my phone and it stops me by grabbing my attention for a feature I never wanted or asked for but was foisted upon me. It may be useful for someone else but it is a problem for me. I am a therapist and my online time with clients gets interrupted by this annoyance. Also, it gives me great concern that someone could be around my machine and see what is happening on my phone or that the MacBook is recording my phone activity while I am away from the office and unable to screen who is around my MacBook. I have HIPAA concerns to be aware of in my work and this is a potential violation waiting to happen.

PLEASE HELP ME TURN THIS OFF.

Why is it that someone at Apple gets these ideas and completely restructures how my equipment works and it's not something I opt-in to have but, once someone does this for me without my approval, I have to run around and figure out how to turn it off to get things working how I want? Something happens with every software update and changes my equipments functionality structure.