Why?

The purpose of a carrot is to store food for the carrot plant so it can overwinter. The leaves are the engine which produces this food so reducing them will have a detrimental effect on the carrots. And as tdscpa says, why do you want to do it? Carrot foliage is very pretty and a healthy row is a thing of beauty :-)

I've read you can trim the top 1inch of carrots to stimulate healthier carrots below. Trimming also helps reduce disease. I guess the other people disagree with this 😎

Actually, there is no proof that trimming back the tops of growing carrots achieves either of those results. As floral mentioned, the foliage grows for a very specific purpose so any trimming is counterproductive.