We shoot through the main umbrella in a portrait for several reasons:
- The umbrella is now closer to the face, making it larger, making the light softer.
- You see a circle as a catchlight, not a circle with a black blob (the flash).
Look at this example – a small part of a recent porttrait, where the main light is a square softbox:
The secondary light (which really ought not to be in the image, ideally) is a reflected umbrella – with the black blob. A shoot-through umbrella would not do this.
Incidentally – focus on the eyes always, and do be sure there is always a catch light (yes, ideally, just one). That makes the eyes come alive: without a catch light, the person looks dull, hardly alive.