This is my take on a question asked on a leadership Q&A page.
Some might be inclined to say that a leader needs to be both task-oriented and people-oriented.
My answer is that it's either-or. It depends on what is expected of the leader.
Scenario 1: The leader is an expert in their field. Initially, they were hired for their skills and experience.
Now, they have the responsibility to show the team how to reach a certain quality threshold. How to perform at a high level of expertise.
They are leading by example. And that requires to be task-oriented since that's what you want from the team following them.
Evidently, a bit of people skills are always required. For instance, the leader needs to possess pedagogical abilities.
Scenario 2: The leader is the manager of the team. Their main tasks include mediation, facilitation, supervision, and development of their teammates.
This leader is accountable for the collective outcomes.
And to achieve team performance requires to be people-oriented.
When leader number one leads by example and through an authority built on skills and experience, leader number two needs a strong understanding of psychology.
Organizations often want to have a leader 1+2.
A leader who has the knowledge of the craft (and is task-oriented because of their background) and can also empower individuals to achieve collective performance.
So they promote their most senior people to leadership positions. They train them with accelerated leadership education and send them back on the pitch.
It rarely works.
A better way to do it is to leverage complementarity.
Create an outstanding duo instead of relying on a mediocre soloist.