I understand that normally CG is placed ahead of COP so that a tail down force can make the aircraft stable. But why can't the COP and CG be placed in the same position so that there needn't be a tail down force to stabilize the aircraft.
I read an answer in Quora saying that "When the CG and CP coincides, the pitching moment will be 0 as the distance between them is 0" What does that mean?
Centre of pressure (CP), by definition, is the point at which the aerodynamic moment of something is zero.
If you are talking about the CP of the whole airplane, then at trim condition, the CG must always coincide with its CP. Period. This is achieved for any operational speed through well designed pitch control that varies in flight. For example, stabilizer/elevator for tailed airplanes, elevons for flying wing.
If you are talking about the CP of a single aerodynamic surface, like a wing or tail, then it gets more nuanced. Let's restrict the discussion to pitching moment only. First of all, CP is not a very useful measure of stability: it always moves around for a cambered airfoil. In fact, at an AOA where the lift is zero for a positively cambered airfoil, it moves to infinity!
Instead, use aerodynamic centre (AC) for stability analysis. For pitch stability, you would like the CG to be ahead of the AC of the entire airplane (this is called the neutral point).
Because:
An aeroplane must have static and dynamic stability in order to be easy to control: with a gust hitting the aeroplane, a statically stable aeroplane returns to a stable attitude without the pilot having to apply a correction. Like a car driving straight when not holding the steering wheel. This answer explains why.
The image is from the referenced answer as well, and shows three centres of pressure: for the main wing $(C_{Nw})$, for the tailplane $(C_{Nh})$, and for the whole aeroplane $(C_{N})$. Note that in cruise, it is no issue if the resulting centre of pressure $(C_{N})$ is on top of the CoG.
It's because normally tailed aircraft (and flying wings) depend on an equilibrium state between opposing pitching forces for static stability, and an inherent tendency of the aircraft to seek this equilibrium state on its own.
So you need a nose down pitching moment that is always present, acting about some "balance point", being the aerodynamic Neutral Point, which is wing CP +/- all other pitching forces also present, like thrust line forces, other lifting forces (like MAX nacelles), drag from things sticking up or down (like floats), etc. ending of at some net location for any given configuration, loading and flight condition. Although a gross oversimplification, you could think of the Neutral Point as a seesaw pivot (although a dynamic gaseous one) for the purpose of imagining it in your mind.
The nose down pitching moment (you at one end of the seesaw) is balanced about the Neutral Point by an equal moment applied at the tail - the tail's downward lift (someone at the other end of the seesaw). The balance of forces for a given configuration will be achieved at some angle-of-attack/speed. At this point, you are "in trim" and the airplane will not want to accelerate or decelerate and will hold a constant AOA/speed/pitch attitude all by itself. It's statically stable.
Move the CG forward and the nose down pitching moment increases, and this requires an opposing increase in tail down force. The tendency to seek an equilibrium state is increased and static pitch stability improves, so static stability is highest at the forward CG limit. Move the CG aft toward the Neutral Point and ND pitching moment decreases (you're moving closer to the seesaw pivot), and tail downforce required for balance decreases, until with CG at the Neutral Point there is no nose down pitching moment and no tail downforce required to oppose it. Whatever equilibrium state there is is very weak or non-existent with the tail largely unloaded, and the airplane will pitch randomly and won't settle down at any AOA/speed/attitude.
Move the CG any farther aft, and now the tail has to start to lift UP, and it all goes to hell and the airplane becomes statically unstable, and eventually uncontrollable.
So, going to the seesaw analogy again (yes it's way too crude but it works for the purpose of visualization for a layperson), you need to be on one end of the seesaw with someone pushing down on the other end, with a force you can control from your end. When you move the CG aft to the neutral point, you've shifted your body to the pivot of the seesaw (CG and CP/NP coincides, as per your question), the person pushing down is no longer needed, and there you are trying to balance it like you're on a tight rope as it wants to tip this way and that by itself in response to the slightest disturbance. The airplane is neutrally stable and is a handful to fly unless it has an active artificial stability system to operate the tail surfaces to mimic natural static stability.
If you've flown an airplane a lot at the maximum aft limit (I did it a lot bush flying) you can really sense this. You still have positive static pitch stability but it's noticeably weaker than with a more forward CG and the airplane can be unpleasant to fly especially in bumpy air, although not dangerously so.
