If by curved you mean concave, no, it isn't. One end is rounded, however, and works well in the "corners" of the nail. The other end has a wedge shape, which you can use either wedge down to merely push back, or wedge up to scrape off the thin cuticle overgrowth like I get way out on my nails. Or you can use that end to clean beneath your nails.

switch to the Sephora brand and buy that one. The rounded tip is for the rounded edge of your nail bed. The straight is to take care of over grown cuticles. You might "shave off" more than you need to if you are not used to this tip.

One end of it is curvy which is to push the cuticle down; the other end is flatter and has a slant to it - that is to clean that same area but press lightly. I got it right by the 3rd nail. HA! Another great thing is that you clean it with alcohol and it's sanitized. You can't beat stainless steel!

You can use the round end to push back cuticles or to get underneath your nails and clear dirt.

Use the round-nail shape edge to push back the cuticles without cutting the skin or your nail. However if you have a stubborn cuticle that does not push back with the rounded edge, carefully use the square shaped edge to cut/push the skin away from the nail.

I had exactly the same problem too, where it was shaving off my nails. It is way too sharp. I would suggest trading it in for the Tweezerman nail tool. It is almost the same tool except it isn't sharp enough to cut into your nails.