> I intuitively understand that if we both write messages at the same time, we will see them in different order.
I think you are thinking like a distributed systems designer. I would assume that if you asked 10 "random Americans" 9 of them would assume that someone managed to send their message first and would be surprised if their phone and their friends phone showed them messages in different orders.
Many people have had the experience of "I tried to call you, but you were calling me!"; I don't imagine they'd be surprised if "something weird" happened when you both tried to send a message at the "same" time.
I think you are thinking like a distributed systems designer. I would assume that if you asked 10 "random Americans" 9 of them would assume that someone managed to send their message first and would be surprised if their phone and their friends phone showed them messages in different orders.