Why is this house built this way? Why does it have shingles/siding instead of brick?

What you're referring to is a wood-framed house with a brick facade. True brick construction, in this day and age, is enormously labor-intensive and can be prohibitively expensive. The brick facade is just that--a facade designed to give the home a brick-house look while incurring the cost of only a single layer of brick attached to the wood framing. You may also see homes that have facades of stone, as well. They're the same type of thing. It should be noted that the choice of a masonry facade has nothing to do with quality of a home's construction. A home with a brick facade can be built as well as any other wood-framed home. It's merely a matter of style. In fact, most builders offer a brick or stone (or even stucco) facade as an upgrade to their basic models.