The day I become a doctor is still a long way off.
Literal
Doctor [to-に] become-can day [topic-は] still far-away.
ほど遠い ('far off, distant') — ほど 'extent' + 遠い 'far' — expresses that a goal is nowhere near achievable yet. まだ ('still') reinforces the distance. The sentence is structurally simple but the combination of aspiration and honesty makes it poignant.