Let's say that the 20% rate applies to income tax, corporation tax, dividend tax and capital gain tax.

When a company allocates $100 to its employee, the employee receives $100 of salary, pays $20 of income tax, and ends up with $80.

When a company allocates $100 to its shareholder, it's first considered as profit, so the company pays $20 in corporation tax, the shareholder receives $80 of dividends, pays $16 of dividend tax, and ends up with $66.

When a company has $100 profit but does not distribute any dividends, it has to pays $20 in corporation tax, so the shareholder value increases by $80, so if the shareholder sells the share, he receives $80 of capital gain, pays $16 of dividend tax, and ends up with $66.

So, yes, if the all the tax rates are the same, you actually end up taxing capital more than salaried income, which would be a big incentive against creating your own company.

This was more true in the past.

Now, companies often put all profits into R&D avoiding both dividend tax and corporation tax. Investors are much more willing to value companies based on growth rather than actual dividends.

But the money the company pays out doesn't count as tax paid by the shareholder, and there is very good reason for this from the shareholder's perspective. The company is a separately legal entity created to protect the shareholder from liability (among other reasons). At least in theory an owner can avoid this "double tax" by doing all business under their own name and accepting the potential liability which comes with that.

The motivation for the OP's argument is that "tax has already been paid" on certain income. It's an arbitrary "rule" put forward by advocates for the wealthy. There's no reason capital gains can't be taxed as income other than: people who make lots of money on capital gains don't want it to be (e.g. the entire hedge fund/private equity industry, along with the budding American aristocracy).

Note: I'm not saying changing the tax rate on capital gains wouldn't have an impact on investment patterns. It would.

"I don't see why capital gains should be taxed lower."

The point of taxing capital gains lower than income is to encourage the wealthy to invest rather than hoard their wealth. This is good because invested money helps drive economic growth which is usually good for everyone.

That seems like a very good argument for taxing wealth.

Not really. We're talking about economic growth not equity. The argument that widespread private investment is better for growth than widespread hoarding is better established than the argument that government spending is better for growth than hoarding. Even with regard to equity or fairness, government spending isn't always better as more government creates the opportunity for more government capture.

There are other arguments for directly taxing wealth, but the one I listed isn't one in my opinion.

The crux of your observation is "fairness"

The crux of our observation is that "we're all getting hosed and you just want to ensure we are getting hosed equally?"

these things can't happen in a vacuum, no matter how much you respect something with the label 'government' on it you do have to factor in what its doing with its passive funding source. Even this article correlates tax policy that benefited the rich with low GDP growth, suggesting that the government would have been a better steward of additional money. It should consider other revenue regimes.

Capital tax is only perpetuated by inequality, as it is a stretch of taxation theory and a mere convenience. The state says "so you want us to take the money now, not gonna say no!" the non-capital class cheers