Think of it this way - I have a car. That car is worth $100 and I want to share ownership. The value of it is $100. I can sell 2 "shares" @ $50, 4 @ $25, etc. But the fact is there will only be that amount of shares. Now say my car is a Ferrari and people want in on it. That will raise the value of those shares. Should I want to make more $, I can release more shares either through an offering or a split. if I do a 2:1 split, you now have double the shares at half the cost. If I want to reign in the shares, I'll buy them back, increasing the cost as those shares are less easily obtained and therefore more valuable.
It's the reason why stock buybacks raise share prices and splits lower prices.
Not really. Splits lower prices proportionately and REVERSE splits raise prices proportionately. And, your car example makes no sense. If shares in the car are bought back, value leaves to buy back those shares. With a fixed value asset (inflation aside), there is no change in value of the remaining shares. In an enterprise such as AAPL, reducing shares through a buyback increases the value of the remaining shares IF the shares can be bought back for less than the present value of future eps.