How about this instead: a manager is a representative of a team, and vice-versa. Not every senior leader in a company has time to get to know and evaluate every individual member of every team; instead, they evaluate a manager as a proxy for the whole team. You, as a team member, will be evaluated through your manager. It's up to you whether that evaluation is positive.
"Make your boss a hero" isn't a very endearing way to phrase it, but it's a concise way to say that in a traditional corporate hierarchy, your fate is aligned with your boss's fate.
I understand it’s different if you’re older with kids and a mortgage or lot of health bills or whatever but I haven’t really felt like my fate has ever been tied to any of my employees.
I feel like it’s just headgames for your manager to try and convince you that making him look good is essential to your career.
Edit: in case this is relevant the shitty project was actually the best project in our department as far as I was concerned before my former manager ran it into the ground by trying to look good by promising dozens of features for people who didn’t use it instead of building something that worked and was extensible
And as a company owner, your fate is aligned with your customers' and investors' fate.
Hence the importance of sales, marketing and investor relations, i.e. managing OUTwards and UPwards.
Therefore the team works hard on things that will make the manager and the manager's managers look great in the woder scope of the company, and the manager says, correctly, that the team is responsible for the work.
I think this kind of manuevering is fundamental to large human organizations with scarce resources (you know, all of them) so the goal is to make it as healthy as possible.
Why? If my bosses boss is happy with my boss then our department gets a bigger budget, more interesting projects and, most important, we get more autonomy and get left alone more. All of those things directly improve my quality of life. If I can keep my bosses boss off my bosses back, then my boss won't be on my back.