Why are color difference signals transmitted rather than R,G,B signals?
Since color transformations are a linear 3x3 matrix, so is converting RGB to YUV and back. Y is needed anyway for compatibility with B/W TVs, and Y signal consists mostly of G component, then mostly of R component, and least with B component, in certain proportions.
As RGB signals have full bandwidth from the camera, so does calculated Y. As human eyes are most sensitive to luminance than color, it makes no sense to waste bandwidth for direct transmission of R or G or B signals. The color signal must also be hidden inside B/W transmission.
Since the RGB to YUV is a linear matrix, you get 3 componets out if you put 3 components in. As the coefficents for calculating Y from RGB are known, the other two components are the ones that describe the other two components U and V.
The U and V components need to contain the rest of the info to calculate RGB, and since Y already contains most of G component, the U and V should contain mostly the R and B components, except the RGB parts that were already sent with Y. That's why the G component is not used. As the Y calculation was done with resistor dividers and analog amplifiers from RGB, you needed to minimize the circuitry, and inside a RGB to Y converter there already exist the RGB components and the weighted sum Y, so easiest thing to do was to also calculate R-Y and B-Y as they would result in larger signals than G-Y. So now the R-Y and B-Y are the signals that contain least luminance info and most color info. And since Y needs higher bandwidth and color info doesn't, the bandwidth of color difference signals R-Y and B-Y can be reduced even more, so that's why none of the R or G or B signals are directly sent.