Part of what I think is pretty exciting about product management is you are a leader from day one in product management. You don't have any formal authority, but you're a leader. You're expected to lead.
Product management is influence without authority
Leadership → Influence Without Authority
You actually have very little true authority because you don't actually manage anyone. A lot of it is all through influence.
We are in the business of influence. Users are doing something, and now we want them to do something else. Our engineers are doing something, and now we want to influence them into building something fast.
Most people don't like product managers often because they haven't experienced good product managers. The core of product management is competency-based.
You have to be willing to take responsibility and it's your job to pick the thing and it's your job to be accountable to your team for picking the thing so you better get it right.
The hardest part about being a leader is when you don't get to just rely on the formal authority. So you're getting to practice all the hard parts about leadership from day one, because you're nobody's boss.
A lot of product management is also managing personalities and figuring out how people want to work with you and figuring out how you work for them.