There isn't a typically path on people becoming CEOs and the same goes for Product Managers.
No two product managers are alike, just like no two products or product teams are alike. Each is unique.
There has been this notion that Product Managers should be like mini-CEOs. While some famous CEOs have had a career in product (i.e Google's current CEO, Sundar Pichai, let's take a moment to explore how we can use the CEO metaphor for Product Management and where we draw the line.
There are many similarities between what a CEO does and what a product manager does. A product manager is not an expert in all the areas of the product team and in a similar way that is the same for CEOs.
Product managers also need to know everything that is going on, but necessarily the need to act on every single issue. CEOs also needs to keep their nose to the ground.
Where I find the most similarity across any scenarios is that great Product Managers like great CEOs are there to manage risks and taking calculated risks. They are often the first and only role where these risks are seen holistically.
Lastly, Product Managers, like CEOs are many stakeholders that they liaise with, get information from and get feedback from.
This is likely where this idea came from -- it's when comparing Product Managers in a startup versus a CEO.
In many cases, and typically before the traction and scale period, the CEO of a startup typically is the defacto Product Lead until which time they have funding to fire a full time Product Manager.
Product Managers at a startup, because the team is small and because the product is the business and the business is the product in the early stages, the Product Manager is really like a mini-CEO.
Product Managers need to be reviewing everything from end to end.
Finally, the responsibility part is where I think this analogy is best served. Product Managers in small and large organizations typically have the full responsibility (though may be not always the authority) when things go wrong. The buck stops with them.
CEOs also have this responsibility at a much greater level, but for product managers in startups it might as well be one in the same.