Note: this answer was made to a version of the answer that was improperly edited and made little sense.
Forces do not converge at points.
You can take a set of forces—any set of forces—with different action points and determine the action point of their sum, which is the point in which all their moments cancel.
Since the force is sum of the constituent forces and the moment (around arbitrary fixed point) is the sum of the constituent moments, you can simply find the moment arm that satisfies the two conditions and that is the action point¹.
Now you can do this with any set of forces, but it may not be useful. In case of aircraft, it is useful to sum the lift forces—their action point is called centre of pressure. And compare it to gravity, action point of which is the centre of gravity.
Summing all down forces is much less useful though, because the set of down forces changes with angle of attack and elevator deflection. As the angle of attack increases, at some point the lift force of the horizontal stabiliser changes from downward to upward!
Note that this point is not the neutral point. The neutral point is the point around which the total moment of lift forces does not change with angle of attack. That however, does not mean that total moment is zero around this point. Quite contrary; for statically stable aircraft, the moment around neutral point is pitching up, and the center of gravity is ahead of the neutral point to balance.
¹ In the general form, the equations are $\vec F=\sum\vec F_i$ and $\vec F\times\vec r=\sum\vec F_i\times\vec r_i$. In the linear case where all arms are along one line (e.g. longitudinal) and all the forces are in the same parallel direction (e.g. vertical), you can solve that as $r = \frac{\sum F_ir_i}{\sum F_i}$, but there is no division operator corresponding to cross-product for the vector case.