Are you familiar with the term "right of way"?

The complaint isn't about a friendly wave. The complaint is that it's someone's turn to go, and instead of going they wave at someone else to insist the other person go out of turn.

The wave is an insistence of "you go first", not a greeting or a thanks.

I do this quite frequently with bicycles caught between lanes. Yes, it annoys the people behind me. But it still improves the situation considerably.

Traffic isn't just 'other cars'.

Do you stop on the roundabout to let cyclists enter the roundabout?

No. That is a net negative. But a cyclist in an unsafe position should be given a path to safety regardless of what happens to other traffic. A cyclist that is not on a roundabout yet is perfectly safe, and stopping traffic on a roundabout to yield to traffic that does not have right of way is not ok.

Ah, OK – that makes sense. In my country, it's not a question of being nice but a part of the road rules. Loosely translated excerpt:

> The driver has the following responsibilities: (...) to do his utmost to ensure that other road users are not endangered, especially the most vulnerable (pedestrians, cyclists and electric scooter riders)

If a cyclist ignored the law and entered a roundabout anyway then I would definitely stop. But if they're waiting in front of a yield sign then obviously not.

I'm not, and after checking the website of multiple driving schools in my country, I guess this is a fairly deep cultural difference - they all mention that you can always let the other driver go first by courtesy, and that adaptation to the situation overrides the base ruleset.

The issue is that very often it would only take you a couple seconds to go through anyway, so you end up forcing the other person to adapt in a way that leaves everyone either the same or delayed.

There are definitely places where letting someone go is appropriate, especially if it's leaving a gap so they can make a turn. But if you're on a road and you have to wave them through then most of the time you're not actually helping, and fake-helping is an annoying thing.