Dropping treated units from the control, or what does Justin Bieber have to do with avoiding vanilla TWFE?

I remember vaguely maybe 6-7 years ago struggling to understand fixed effects and diff in diff from a traditional perspective. I saw diff in diff as really about just comparing trends. Take two groups, calculate their trends, and subtract one from the other. Hence the name: difference in the differences.

It was then eye opening for me to see a table in …