Most fields are troubled with title inflation, sometimes out of necessity, however, often out of vanity. But it feels like product management is out of hand. I am sharing my personal 1-line litmus tests I use to ratify titles. I don't expect everyone to agree with these - use it or refine it as you see fit :)

You aren't a Director/VP of Products until:
you have put a pen-to-paper to craft an unassisted and independent narrative, roadmap, and forecast as to when, why, and how the portfolio of products in conjunction with the company's rest of the operations will impact the earnings

You aren't a Product Owner until:
you have complete access and at least a shared authority to make financial (funding) decisions for the product

You aren't a Product Manager until:
your span of control ranges from the responsibility to address "Are we building the right product?" to the accountability to solve for "Are we building the product right?"

You aren't an Associate Product Manager until:
you have demonstrated self-imposed accountability to do what's right for the user based on research-driven insights that you have shared ownership to cycle from concepts through experience all the way to engineering and launch