From my limited understanding of Thomson scattering, it only works for wavelengths comparable to the size of the electron. Because scattering was observed at a variety of wavelengths, it was assumed that the size of the electron must change when rays of different wavelengths were scattered off of it. One of the merits of the Compton Effect was that it described this phenomenon without imposing unlikely constraints on the electron.
But I don't understand why? Why does the scattering only work for certain wavelengths? And how exactly does this transfer into the idea of an electron of variable size?