1. I have failed to train the manager properly, and need to consider whether that's because I'm a bad manager or the environment is such that it's time to leave; and
2. If I have spent some effort with my team and this manager to prevent such idiocy, the manager who made the decision needs to be either demoted or fired.
This is a more common scenario in customer service than it should be. The fact that seniority was the only criteria is an indicator that it's not a good environment. The fact that this manager thinks she needs to lecture the woman who quit on "professionalism" (especially for the reasons stated) is an indication that it's a terrible environment.
But I'm inclined to believe this is someone trolling "ask a manager." In what customer service job does someone with six years' tenure have lowest seniority?
I don't know the site this is on. Is it a reliable one? If not, I bet this is a marketing stunt.
I'm not 100% sure that this is one, though - there are some red flags but I've definitely had managers I could imagine doing this. And I can see the point in printing the letter even if you think it's not real but that someone out there might do the same thing for real.
The whole thing is fiction, plain and simple.