Issuing new shares is dilutive.

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Stock buyback example:

There are 10 shares of ABC Corp, it has a market cap of $100. Each share is worth $10.

ABC corp buys back one share and destroys it, leaving 9 shares.

$100/9 shares=$11.11 per share.

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Dilution example:

There are 10 shares of ABC Corp, it has a market cap of $100. Each share is worth $10.

ABC corp needs $10 so they sell one additional share which the board has authorized. There are now 11 shares.

$100/11 shares=$9.09 per share.

Mechanically, from a corporate finance perspective, the price per share doesn't change. Equity decreases or increases by the amount of the buyback or issuance. So in your example, a buyback of 1 share means equity becomes $90, and each share is still worth $10. Likewise for dilution, equity goes up to $110, share still remains at $10. The dilution refers to the ownership of the company, not the stock price.

However, in markets, a buyback is a positive signal (with increased EPS also) that can increase the share price.