The company is owned by the investors that bought the stock and those investors want their investment to go up.
If the stock goes down investors can fire the current company management since they are the ones that own the company.
Company management cares about their jobs so they keep the investors that own the company happy by keeping the stock price the same or making it go up. Often times a lot of the highest management and employees also have some company stock, which makes them also care about a good stock price.
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