If business owners, taxi owners, hotel owners and others who claim to be working for themselves need to depend on customers and customer satisfaction for profit, that is to be able to get money from them, are they really working for themselves?
Maybe the people who are actually working for themselves are those who do not need people or to satisfy any customer to make profit, example like the traders who do not need to lure customers to their shop like business owners or hotel owners, or taxi owner that need to follow instructions from their clients etc.
What could be the real definition of working for yourself?
A very good question indeed.
If you own your business, I don't think it's incorrect to say you work for yourself just because you still have customers to please.
But I think owning a business is much overrated in terms of the difference between that and working on an employment contract. Often times, the latter is much better (especially in jurisdictions with extensive employee protection laws).
Let's take a simple example: You are a full-time cleaner employed by ABC Ltd to clean its office Vs. you own a cleaning business, i.e. you still do the same job but as self-employed. In both cases, the work that you do is exactly the same, but, as an employee, you get holiday allowance, sickness leave and a legal protection against unfair dismissal (depending on the jurisdiction of course) among other benefits. In the self-employed scenario, you would ususally get more payment on hand, but you would be responsible for all the national insurance, pension contributions and making provisions to cover for any absence, but you would get very little protection from the conrahent not paying you on time or from them terminating/or not renewing the contract.
People like to think that "owning a business" is some holly grail that automatically grants you more freedom since you have no boss telling you what to do, but, in practice, is often the opposite, especially when you're dependent on one or few major clients who might have much higher and maybe even unrealistic expectations as compared to having a boss.