I can see how a share buyback would put upward pressure on the share price, but how could it have a positive effect on earnings? Seems like it would have to have a negative effect on net earnings over the long term if the buyback was financed via a loan, due to the need to repay the loan.
And EPS is one of the big metrics for share prices (the PE ratio uses it for example). It makes sense that if there are less shares they should all be worth more, but EPS is the reason why that is the case.