Slice off the tops and bottoms of the grapefruit, then cut off the skin. Section fruit and remove membranes, working over a bowl to catch the juice. Add oil, vinegar, salt and pepper in bowl; whisk to combine.
Toss the arugula with half of the dressing. Arrange arugula on plates, then top with grapefruit, avocado, and red onion. Spoon on the remaining dressing and serve.