Selling stock means selling a portion of ownership in your company. Any time you issue stock, you give up some control, unless you're issuing non-voting stock, and even non-voting stock owns a portion of the company.
Thus, issuing (voting) shares means either the current shareholders give up some of their ownership stake, or the company issues stock it held back from a previous offering (in which case it no longer has that stock available to issue and thus has less ability to raise funds in the future). From Investopedia, for exmaple:
Secondary offerings in which new shares are underwritten and sold dilute the ownership position of stockholders who own shares that were issued in the IPO.
Of course, sometimes a secondary offering is more akin to Mark Zuckerberg selling some shares of Facebook to allow him to diversify his holdings - the original owner(s) sell a portion of their holdings off. That does not dilute the ownership stake of others, but does reduce their share of course.
You also give up some rights to dividends etc., even if you issue non-voting stock; of course that is factored into the price presumably (either the actual dividend or the prospect of eventually getting a dividend).
The impact on stock price of course is also a major factor and not one to discount; even a company issuing non-voting stock has a fiduciary responsibility to act in the interest of those non-voting shareholders, and so should not excessively dilute their value.