> That's a bad analogy. It wrong because you can see what doors, cupboards and drawers are available for the public. Doors that are in-reach but that shouldn't be used by the public have signs like "restricted access" or "employees only". You can't do that with the internet. You can't see that a port is not available to you until you try it.
But you can see what ports/doors are available. TCP doors are defined in the RFC and they are numbered 0-65535. Those are the ones available.
Port scanning still is analogous to trying all these doors and see which one are open.
Just because it is a lot of doors to choose from doesn't make it very different. That's why guests ask a host where the bathroom is.
When you visit a website, it's not very cool for that site to check which of all your TCP ports are open. It's none of their business.