>As a manager, the company comes first, the team second and the individual third.

I think managers should take a little more nuance into this equation.

As a manager you sit between the interests of the business and the interests of your reports. Depending on the context the hierachy might actually be individual/team/company.

If you keep the model of company/team/individual, you will be seen as great at "managing up" (in this case also you might be seen as a "suck up"), decent at managing across departments, and your team will probably think you could care less about them.

There will be many times where this hierarchy changes and knowing when/how/why those changes happens will take you to next level management.

E.G. In a 1:1 with your report _they_ are a priority. (managing down)

In a company wide address on team performance, the needs of the company+the team need to be addressed. (managing up and across)

In an executive meeting, the needs of the company are paramount (managing up)

etc etc.