I'll let you in on a little secret. I hate shredding cheese. I have back problems and the constant up/down motion, especially for softer cheeses like cheddar, really starts making the tender spots hurt after a while. Shredding my own cheese was, however, one of those things I picked up very early on in the cooking journey and did it for years. After the dishwasher melted the handle on my very favorite grater (a rotary type grater with a coarse drum - proving difficult to replace), I quit shredding my own cheese in lieu of pre-shredded cheese. But a few months ago I stumbled across a good deal on "block" cheese and decided I'd try to shred my own cheese again.
So why do I shred my own cheese? Lots of reasons.
For starters, pre-shredded cheese has lots of additives in it to prevent it from caking and sticking together. Potato starch, corn starch and powdered cellulose are the most common. Now in general, I prefer not to eat a lot of additives with my food, but powdered cellulose is particularly egregious. It's essentially wood pulp. In its truest form, that wouldn't be so bad, I suppose. If you WANT to eat sawdust on your pizza. But powdered cellulose isn't wood pulp's true form. It's wood pulp that has been chemically treated to extract the fiber. And frankly, I especially don't want to put unnecessary chemicals in my body.
Pre-shredded cheese, because of the additives, doesn't melt as well as cheese you shred yourself. What this means is if you want to make a cheese sauce, melt cheese into a cream based soup, or stir it into a casserole, pre-shredded cheese isn't going to melt and meld with the rest of the ingredients. In a soup, you might even find your cheese has clumped up and settled to the bottom of the pot.
Now here's the tricky one: shredding your own cheese is cheaper. I've done some price comparisons and have found that ounce per ounce, a bag of pre-shredded cheese costs the same as a "block" of cheese. However, I find that I use less cheese when I shred it myself and still get all (or sometimes) more of the cheese flavor. Also the block of cheese will last longer because it has less surface area for mold to find and latch on to. Once your shredded cheese has gone moldy there's not much you can do about it. If your block of cheese gets mold, you can safely cut off the molded part plus about 1/2 inch and salvage the rest of your cheese.