Part of what makes cut-out cookies tricky is that the dough gets worked more than simple scoop-and-drop cookies. With more action, you get more gluten from the flour and this can make your cookies tough instead of tender.
When rolling out the cookie dough, always start with your rolling pin in the middle and roll outwards. Repeatedly rolling back-and-forth or side-to-side tightens the gluten more than long strokes from the middle.
You’re also not working so hard when you roll from the middle. The dough is constantly being stretched outwards instead of getting pulled back on itself. You end up using fewer strokes and are finished more quickly without overworking the dough.
Give this a try the next time you make cut-out cookies and see if it helps!