> There was a price at the current supply and demand. Buybacks increase the demand which increases the price.
The company has a value. If the P/E ratio gets worse because the share price went up with the same earnings, more investors will find it profitable to cash out and invest in something with a better ROI. That doesn't happen instantly, but it happens quickly, because cash-flush investment banks realize they can front-run the correction for a profit, which makes it happen.
But the buyback itself often actually improves the ROI of the company and legitimately makes it worth more, because the company itself was getting high returns on its productive capital and low returns on its cash, and now less of its share value is represented by the low productivity cash.
> That is what people who have problems with buybacks but not dividends, would like to see happen
Except that then the perverse incentive for managers becomes to boost the stock price by not issuing dividends, since dividends reduce the stock price. The only real way to fix it is to fix their incentives, and once you do that you're back to preferring buybacks due to the tax treatment.