An accelerated charge emits radiation and so must lose energy. This implies that it feels a "reaction force" in the direction opposite the motion. Since EM interactions conserve energy/momentum, it must be possible to describe the reaction force in terms of EM fields acting on the charge. These fields must be generated by the charge itself- we may assume that any external fields are uniform. Now, we know that the fields at any point can be found by integrating a function of the charges & currents along the past (or future) light-cone of that point- the "retarded time" integral. But our particles world-line is of course timelike, so it never intersects the light-cone of any point on the path! So how can the particle produce a force on itself?