That is true, but it's irrelevant here. When you use your skills to increase your productivity, it's your productivity that gets increased, not someone else's, even if they have similar skills. That is the sense of exclusive ownership that is relevant to this discussion.
> A capitalist can and will use the force of the government to stop others from using the things he has laid claim to
So can a non-capitalist. Anyone who is willing to use the government as a tool to further their own ends can. That is a much broader set of people than "capitalists".
> A capitalist can create capital out of thin air by making money
No, that's not what creates capital out of thin air. What creates capital out of thin air is creating something that increases productivity. Just "making money" does not do that. Money can of course help with creating something that increases productivity, but it can't be done just by making (or spending) money.
> and use the force of the government to stop others from making money.
Again, this is not a problem of capitalism, it's a problem of corruption: people using the government as a tool to further their own ends.
> Right now I think it is mainly unskilled workers who are changing sectors, as they are the ones who can benefit most from it.
I don't think this is true. Skilled workers are far more likely to be underpaid as compared to the productivity they are capable of.
> As for skilled workers, they have already climbed a few steps on the ladder.
I don't think this is true either. Skilled workers very often are not able to climb on the ladder, because their skills are not being recognized or compensated properly as compared to other skills that ladder climbers have, like schmoozing and taking credit for other people's work. And once they recognize this, they are far more likely to be both willing to and capable of finding a better job that compensates them better for the skills they have.
You can never exclusively own skills. If somebody else achieves some skill or knowledge that I have, I cannot use the force of the government to stop him from having those. A capitalist can and will use the force of the government to stop others from using the things he has laid claim to: Land, natural resources, equipment. A capitalist can create capital out of thin air by making money, and use the force of the government to stop others from making money.
That's the difference that matters.
> Try doing that as an unskilled worker and see how far you get.
Right now I think it is mainly unskilled workers who are changing sectors, as they are the ones who can benefit most from it. If your job cannot get worse, there is no reason not to change. As for skilled workers, they have already climbed a few steps on the ladder.