Not sure who "you" is but the company will have fewer shares outstanding, investors who don't sell will have the same and those investors will also now own a greater % of the company as well as a greater earnings per share.
> If you "reinvest" in the company you give up all the proceeds you received to buy back the shares that you just sold to the company
I am 100% not saying that as that would eliminate the benefit. The benefit is to long term investors who buy, hold and reinvest dividends and reinvesting dividends to buy more stock is key as that is where the historical exponential returns are because it increases your ownership share and future dividends.
That is where my example numbers come in because you can only reinvest to buy more shares and thus your ownership % the dividend amount minus tax amount whereas the company can spend the entirety of a dividend buying shares to remove them from the outstanding market. The difference between those two numbers (1.05 and 1.04 in my example) then compounds and effectively goes towards increasing share prices which do eventually get taxed but they get the benefit of compounding while the owner holds.
Also, while you need quite a few shares, you can estimate and sell the percentage of shares a company is buying back in order to keep the same % ownership thus acting like a dividend so I myself would prefer all companies I invest in to never give out dividends and only do buybacks unless their P/E ratio is truly absurd.
In most cases in the past decades, buybacks were accomplished using loans rather than profits, leaving the companies in worse financial positions. More than half of the companies that engaged in buybacks in the past decades are either bankrupt, declared bankruptcy in 2020, or are underperforming the market. Only a handful of companies that engaged in buybacks are doing okay, and those companies also issued dividends (see for example, Microsoft).
With a buyback, you have fewer shares after the buyback. If you "reinvest" in the company you give up all the proceeds you received to buy back the shares that you just sold to the company. But you've paid taxes as a result of the initial buyback so you have less money than you received to reinvest, and now presumably the shares are all more expensive as well. Your position is economically worse off if you reinvest than when you started, because you have the same amount of shares (or fewer) but paid some tax to get there.
With a dividend, you can keep the dividend, or buy more shares of the company or some combination of both. Your economic position is improved either way regardless of the amount of tax you pay.