So once you get over the image of all those skinny pigs and cows doing aerobics, you need to re-learn roasting. It can be the cut itself. If it's from a part of the animal that got a lot of exercise, the fibers are big and tough. Keep in mind that some of the cuts that used to make a good roast don't anymore. Spring for a more expensive cut and grade to roast, and save the rump for a pot roast or a braised dish that cooks in liquid.
Meat contains lots of water.
While you're roasting it, that water evaporates in the hot oven. At 180 degrees, almost all of the moisture in the meat is gone, so you have perfectly dry, perfectly tough meat. That's the cooking that continues after you take the roast out of the oven. It easily can add 10 degrees to the temperature of meat and turn a perfect medium into well-done shoe leather. Nothing causes more angst.