Step 1: Understanding the Question:
The question wants the substituent that sends further substitution to the meta position rather than to ortho or para.
Step 2: Key Concept:
A group directs ortho and para whenever it can donate a lone pair into the ring by resonance, even if it is inductively electron withdrawing. A group directs meta only when it withdraws electron density with no compensating resonance donation.
Step 3: Detailed Explanation:
F, \(NHCH_{3}\), and \(NH_{2}\) each have an atom bonded directly to the ring, fluorine or nitrogen, that still carries a lone pair able to resonate into the pi system, so all three activate the ortho and para positions to some degree. \(CF_{3}\) is different because its central carbon has no lone pair, so it can only pull electrons away inductively through the carbon-fluorine bonds, leaving the ortho and para positions comparatively more electron poor than the meta position.
Step 4: Final Answer:
\(CF_{3}\) is the meta directing group.