I suspect none of us can comment much as we were not there, and in such cases, different people may well perceive each other’s behaviour and tone as well as their own in different ways. On the factual bits, 20 minutes is the official and advertised gate closing time so when you say you were there 20 minutes before bear in mind that on their official system it could easily be 21 or 18. Offloading pax at t-20 is not an over reaction, it’s what they are asked to do if boarding is otherwise complete. Can you give us more context as to why you made it to the gate so literally last minute? Was it a late connection or did you just arrive or leave the lounge a bit later than would have been wise?

on the tone etc, if you feel the agent was unprofessional, you can complain via the website. If multiple complaints have been raised about the same agent BA may well investigate and take appropriate action; if your complaint is isolated, it may suggest your threshold for heckling is lower than for many other passengers.