I am employed and I earn my own money, but I am not truly "independent".
The OP means that if you earn your own money, then you do not depend on your spouse for income. This provides you with more freedom than you would otherwise have. Both because you can divorce and still have income, and because your spouse can no long argue "This money is earned entirely by me, so I have complete discretion over how it will be spent".
What economic system do you propose that has the most individual independence?
All of the greatest problems looming on our horizon are tied to how we organize production and consumption.
Because I asked about it, and you answered by confidently describing it, instead of saying "it doesn't exist."