I know what is happening with my body by watching the numbers in my workouts: how much I'm squatting, how long a 400m run takes me, and so on.
If you're bulking or cutting for the sake of appearance, then vanity is the goal and measuring body parts is just part of the territory. If you are bulking or cutting for performance (ie, bulking to get stronger or cutting to get faster), then I'd again argue that monitoring the numbers in your workouts tells you more about the success of your weight change than the exact size of various body parts. For example, if I'm cutting and see my barbell lifts decreasing, then it is very likely something is wrong (I'm cutting too fast, not getting enough protein, or not lifting enough). On the other hand, if I'm cutting and see my biceps have gotten 0.5" smaller, what the hell does that tell me? It might mean something is wrong as above, but it could also be that I lost water weight or fat from my arms. If I'm bulking and see that my thighs got 1" bigger, that might mean I got stronger, but until I try to squat, I won't know, so the size measurement is not all that useful.
Of course, I once again must point out that I'm not saying to ignore appearance metrics completely. You've got to keep things within reason. If you are cutting and your arms shrink 5", that IS a good sign that something is probably wrong. And there are cases where the body measurements are part of the "performance": for example, in sports with weight classes, your exact bodyweight and composition are obviously crucial.