While it's easy to prove rigorously I think the easiest way to think about it is to think what number/numbers could go between 0.9 repeating and 1.
I guess that it also requires a second thought experiment that if no numbers can go between two numbers, those two numbers must be the same.
edit: this might be even easier:
1/3 = 0.333... -> multiply both sides by 3
3/3 = 0.999...
1 = 0.999...
Let's say your great-great grandfather stole bricks from a victim to build a factory that you now own and that provides a nice living. Because of that the victim was not able to build a factory and their descendants are poor.
Let's say this crime is very well documented.
Did you do the crime? No. Are you reaping the benefits of the crime? Yes.
Should you give that factory to the descendants? Should you be required to help the poor descendants? Would it be a nice gesture to help the poor descendants?
Nobody is asking for the factory. People are asking for a bit of help because it's clear that you are still reaping the benefits of a crime that was perpetrated by an ancestor and the victims descendants are still feeling the repercussions of that crime.