My brain doesn’t have to understand its own workings in order to work. Even a frog can see a fly, hop toward it, and catch it mid-flight with its tongue, all without knowing how its neuromuscular apparatus accomplishes these feats. I don’t know through introspection how I see and run and catch a ball, how I feel warmth or hunger or sexual arousal, how I understand spoken language or remember the name of my elementary school. Why should I expect my ability to decide and to take intentional action to be any more accessible to introspection than any of these other neurological functions?
Humans are at least partially aware of their own limitations. I don’t have much body fur, but if I turn on the heat inside and put on a coat when I go out I can survive in a cold climate. I can’t outrun a zebra, but if I get in my Jeep and drive after it I can overtake the zebra. I have a hard time remembering a 9-digit number, and even then my memory degrades rapidly, but if I write the 9 digits down I can retrieve them when I need them. Humans build and use tools largely to compensate for their mental and physical limitations: this ability is paradigmatic of human intentionality.
Cognitive psychology as an empirical subdiscipline emerged in the late 60s not from philosophical idealism but from behaviorism, which regarded all behavior as an automatic stimulus-response mechanism unmediated by thought. Cognitive psychology presented empirical evidence supporting the alternative contention that there is a black box intervening between S and R, processing inputs and preparing outputs. Neurologists are exploring more directly how the black box works. But explanation won’t change functionality. When Copernicus figured out that the earth rotates on its axis and revolves around the sun, and when Galileo confirmed the heliocentric system observationally, people didn’t suddenly spin off the surface of the world and float into space, nor did they suddenly stop seeing the sun rise in the east and set in the west. If a satisfactory empirical explanation of intentionality is achieved, that won’t mean that people will suddenly stop intending or realize that they’d never in their lives actually intended anything.