Not asserting high status, or taking too much credit, or claiming privileges can be an important part of cooperating and working well with others.

I agree so hard with this. I think that general humility is a pretty good strategy for getting people to cooperate with you. Never lie about what you think, but don't overtly grab status or you will set off people's alarms.

If you disagree, don't flaunt it or people will become defensive, and after that most people will treat arguments as soldiers and not listen to you in the future.

Presenting yourself humbly, rather than as someone who's just better than everyone else, can make your success seem more accessible to other people and encourage them to follow in your footsteps.

It also makes people want to work with you. On my robotics team I pretty much always solicit input on decisions, and aside from making it easier for me to think, and resulting (IMO) in better decisions, it also made people want me to lead them.

To the point that I ran for President unopposed.