Why do GMs repeat moves instead of offering a draw? Watching recaps of the 2021 Candidates Tournaments, so many games end in consecutive repeating moves. I have a general impression that lots of top level games are drawn by repeating moves. Why do the grandmasters do this instead of offering a draw?
A repetition giving the opponent the opportunity to claim a draw is a de facto draw offer but not a de jure draw offer.
What does that mean? Well the &quot;de facto&quot; part means that in practice it has the same effect as a formal draw offer while the &quot;de jure&quot; part means that legally it is not a formal draw offer.
Psychologically it makes a subtle difference but practically it makes an important difference. The difference is the legal aspect. Why is this important?
According to article 11.5 of the FIDE Laws of Chess:

11.5 It is forbidden to distract or annoy the opponent in any manner whatsoever. This includes unreasonable claims, unreasonable offers of a draw or the introduction of a source of noise into the playing area.

Normally arbiters interpret this to mean repeated draw offers in a small number of moves. That is why you are instructed to notate your game as follows in Appendix C.12 -

C.12 The offer of a draw shall be marked as (=).

Repeating the position does not constitute a formal draw offer and so cannot be part of a claim of disturbance due to repeated draw offers.

What do you think the psychological difference is?

When you ask for a draw you are a supplicant. It's like you are asking for a favour. &quot;Will you please give me a draw?&quot;
When you repeat the position you are saying something completely different which is why in some positions the experts advise you to repeat once (so no possible draw offer) to demonstrate dominance, let the other player know who is the boss.
If you are a much lower rated player and you repeat twice in a forcing situation you are effectively saying &quot;What ya gone do, punk? Repeat and give me the draw? Or deviate, play a bad move and give me a chance to win?&quot;
I have won several games with that exact tactic. It's surprising when it works but some players have more ego than common sense. It's like their response is something like &quot;No way am I accepting a draw against you. I'm so much better than you that I can beat you from a losing position&quot;. I have to admit I've been on the opposite side too. I've played a bad move rather than accept the draw and I've paid the price.