When installing a street elbow, should the male (smaller) end always point where the water is going?

No, the male (smaller) end of a street elbow doesn't inherently point downstream or with the water flow. Its purpose is to connect. The male threaded end always screws into a female fitting, while the female end of the street elbow receives a standard male threaded pipe or fitting. The direction of water flow is determined by your overall plumbing layout and source, not by the specific orientation of the street elbow's male end relative to the flow.