It does reduce prices because it increases the supply of available shares, it's just that reducing prices isn't necessarily a bad thing. We want the prices of bad things (e.g. frauds) to go down and more generally we want prices to reflect reality which happens more effectively when informed investors can express negative views through shorting.

It's worth adding the qualifier that increasing the supply of available shares need not reduce prices at all if there is enough demand to buy shares at the original price (which there should be if the price is definitely correct and the market is efficient enough). Even without perfectly efficient markets the shorters don't make money if enough other market participants think they're wrong

> if there is enough demand to buy shares at the original price (which there should be if the price is definitely correct and the market is efficient enough)

That's true in a weird abstract "perfectly efficient" world where nobody has to buy or sell stocks except for liquidity, and we all just know the correct price.

The normal model of the market posits that different people have different biases and scraps of information, and we use buying and selling to find the "correct" price. Under that model, selling will always reduce the price compared to what it would have been.

The process of shorting involves selling shares now with the intent of buying shares later. Price will drop in the near term bc you're increasing supply. In theory, without short selling, the market would still eventually arrive at the correct price, but short selling expedites the process.