You don’t have to whisk mayonnaise by hand. It’s easier and quicker to do in a blender.
You do still have to go extremely slowly with the oil.
Basically, you’re forming an emulsion, which means you’re trying to get each molecule of base (in this case egg, and in the case of salad dressing, vinegar) to be completely surrounded by fat molecules. If you introduce the fat molecules too quickly, they will just glut the mixture and not surround the central molecule in an orderly fashion. Then you will have a mess.
You need both an emulsifying agent (mustard or egg), and to whisk continuously. Both those steps ensure the molecules line up properly.