Actually a person might pursue all but (c) an illness.
Pursue can mean multiple things including “to follow in order to overtake, capture, kill, or defeat” (Merriam-Webster). This would apply to (b) a runaway horse. Pursue could also mean to find or employ measures to obtain or accomplish; seek” (Merriam-Webster). This would apply to both (a) an education and (d) a career. The only thing someone cannot pursue is an illness.