It may be easier to see this if you think of the new investment as being in a start-up computer company--a company that is doing research, building a new plant, hiring employees,,,,and won't make money for years.  Perhaps you would see the new company as a "real" asset.  In that case the holder of the auto company, let's say GM, stock, faces the very same decision I outlined.  Sell $5million of GM shares, pay $2million in taxes, invest the remaining $3 million,,,,,and his net worth is now $8million rather than $10; his dividend flow which he lives off of is $150,000 rather than $300,000; and some might think the $3 million he invests is in a highly risky asset--in fact it is,,,we just know with hindsight that it is the way to go.  many startups fail, and you lose it all.  One element of the decision for the investor is that in one option he can pay 0 taxes, and stick with his original investment.  In the other option he can pay $2 million in taxes, and lower his net worth to $8 million, and hope the new investment will more than offset that.

I'm just trying to demonstrate the way the economic incentives work,,,and show that capital gains taxes work against the free flow of investment dollars, which is a key component of what drives the economic growth, new jobs, etc, in our society.  The higher the capital gains tax, the more the incentive to stick with your current assets with large unrecognized capital gains; the lower the capital gains tax, you are more likely to move your investment dollars around to the most promising investments, which are likely to drive economic growth.

You said above

to pay a tax out of the income flow they are appropriating than there is for those who receive labor or rentier income.

 There is an important distinction here between these two.  With a capital asset, there is no income flow--so is not a question of a tax being paid.  The owner holds the asset, and it may grow or decrease in value,,,,,but there is no transaction to be taxed.  (Except in the case of a dividend being paid on a stock, and in that case the income flow is taxed.)  Labor and rentier income are in fact income flows, generating cash, and that in most systems are when taxes are applied.  In general, owners of capital assets have invested that money, and are foregoing the spending of those investment dollars.  Rentiers are collecting rents, and can spend the cash as they please;  same with laborers.  (Note most people are both--investors and laborers.)  

The policy argument I'm trying to focus on is the different investment incentives, and consequences, of taxing the gain on capital assets.  If capital gains are taxed at 70%, there is an enormous incentive to hold onto assets; at 50%, less so; at 25% less so; at 15% much less so; and at 0%, money goes to the most productive assets.  (there are many more issues, and I'm using simple examples to focus on this point.)