Recent investigations of how the median size of extragalactic radio sources change with redshift have produced inconsistent results. In a previous investigation Eales compared the radio and optical properties of a bright 3C and a faint 6C sample and concluded that for a universe with Ohm(0) = ODmed proportional to (1 + z)(-1.1+/-0.5), With D-med being the median size of the radio sources at a given epoch and z the redshift. Oort, Katgert, and Windhorst, on the other hand, from a comparison of the properties of a number of radio samples, found a much stronger evolution, with D-med proportional to (1 + z)(-3.3+/-0.5) for Ohm(0) = 0. In this paper we attempt to resolve the difference. We have repeated the analysis of Eales using the much improved data, in particular, the virtually complete redshift information that now exists for the 6C sample. Confining our analysis to FR 2 sources, or ''classical doubles,'' which we argue is the best understood class of radio sources and the least likely to be affected by selection effects, we find D-med proportional to (1 + z)(-1.2+/-0.5) for Ohm(0) = 0, and D-med proportional to (1 + z)(-1.7+/-0.4)for Ohm(0) = 1. Moreover, in contrast to earlier studies, we find no intrinsic correlation between size and radio luminosity. We show that there is a selection effect that affects studies of this kind, the magnitude of which has not previously been realized and has likely led to an overestimate in the strength of the size evolution found in previous investigations. Our complete redshift information allows us to gain insight into our result by plotting a radio luminosity-size (P-D) diagram for the 6C sample, the first time this has been possible for a faint radio sample. The most obvious difference between the 3C and 6C P-D diagrams (i.e., the radio astronomers' H-R diagram) is the clump of sources in the 6C diagram at D similar to 100 kpc, P-151 similar to 10(27)-10(28) W Hz(-1) sr(-1). These clump sources have similar sizes to the emission-line regions found around high-redshift radio galaxies, suggesting that the presence of dense line-emitting gas around high-redshift radio galaxies is responsible for the size evolution. We show that this explanation can quantitatively explain the observed size evolution, as long as either there is little X-ray-emitting gas around these objects or, if there is, it is distributed in a way similar to the distribution of the emission-line gas, namely, highly anisotropic and inhomogeneous.