>It’s not so simple. In a perfect market, the market value of the company will go down when company buys back stock. Why? Because the value of the cash is now gone. So in your example, each stockholder just owns a slightly larger piece of a slightly smaller pie.

That's not right. You have a larger piece of a smaller pie, but you have the same amount of pie.

Edit: the confusion is you are talking about total market cap while the parent is talking about share price. Total market cap is irrelevant to stockholders. Share price is all that's relevant.