I don’t even really know where to start. First is probably that you don’t get to define words on a whim and that your definition of both capitalism and socialism lacks understanding. Just read the Wikipedia entry for both and you’ll find them better defined within the first sentence of their respective entry.
And honestly I’m too tired to properly explain all the traps you fell into after that so good luck with your Libertarian socialist dream or something idk
Not accepting Wikipedia as some reasonable baseline for truthful or commonly accepted definitions is the sort of hill I wouldn’t want to die on but sure. Especially for content that is so politically contentious Wikipedia usually settles on a reasonably holistic description where other outlets will leave out downplay or politically color certain parts of definitions, obviously this happens there too, but it’s more likely to be corrected especially on divisive Issues. I mean you can go ahead and read the discussion page related to a topic and find out why and how sections came to be.
I’m not trying to lecture you I simply think that having any discussion is impossible if there is no shared understanding. Which is why I deferred to Wikipedia simply the most common database of knowledge in the world. The articles there might show me to be ignorant, but unlike you I’ve at least read parts of them with the intent to understand the information provided. Which I do to some extent not to completely accept what is said there but just to effectively communicate with other people, because Wikipedia gets close to a common definition for anything you might be talking about.
It’s not about a completely factual definition because the topic is way to complex and nuanced to have one that isn’t at least several long books, everyone lacks understanding of the topic because it’s impossible in many ways to have a complete understanding of it. That’s why it’s a philosophical topic and not a natural science, the topic is currently completely impenetrable for the scientific method alone.
It is interesting and important to discuss precisely because it’s so hard to grasp, so multifaceted and so central to all of our lives at the same time. And as I said before if we can’t agree on baseline definitions all that potentially interesting discussion is lost on us.