In the course of getting work done at a company, nobody should be doing anyone else any favors. Everything you do at work should be the most important thing you could be doing to add value to the business, and those things should be aided by people whose job it is to support that prioritized effort.
In the course of doing work, favors are either misunderstood responsibilities, gaps in company process or design, or people working on non-priority things:
Sometimes someone will say “I’ll help you out here” when really it’s just their job. Them saying they’re helping you out is either an exercise in self-marketing, a power move, or confusion.
Sometimes someone will say something like “Alice really did me a favor in onboarding me so well”. But if Alice has to onboard you as a favor, that’s a gap in your team responsibilities that needs to be fixed.
A subset of the “Don’t Do Me Any Favors” mantra is Employees Don’t Get Charity - business and managers should never claim to be doing something altruistic for their employees. People don’t want your charity, and if you’re doing something for your employees it’s almost certainly not charity and instead a reward that you are giving them because they’ve earned it, or an action you’re taking to help your team, which is your job.