@clacke According to Collins, the words don't quite mean the same thing to British people and American people:
https://www.collinsdictionary.com/dictionary/english/egoism
https://www.collinsdictionary.com/dictionary/english/egotism
I wonder if your correspondent isn't on the same side of the Atlantic as you.
In either case, the two words do look pretty similar! Honestly, I wouldn't waste too much time over a dictionary snipe, if that's the way it came across.