If each pixel contains the channels for the 3 primary colours, why can a 1-bit picture only be presented in white and black?
Please read the Wikipedia article 8-bit color.

8-bit color graphics are a method of storing image information in a computer's memory or in an image file, so that each pixel is represented by one 8-bit byte. The maximum number of colors that can be displayed at any one time is 256 or 2⁸.

In other words, the problem is that 8 bits mean that all three primary colors red, green, and blue, are encoded in 8 bits in total.  From Wikipedia:

The simplest form of quantization frequently called 8-bit truecolor is to simply assign 3 bits to red, 3 to green and 2 to blue (the human eye is less sensitive to blue light) to create a 3-3-2
Bit    7  6  5  4  3  2  1  0
Data   R  R  R  G  G  G  B  B

8-bit color image, but this process is sub optimal. There could be different groupings of colors that make evenly spreading the colors out inefficient and likely to misrepresent the actual image. Because the color map doesn't need to have every color in it and just needs to accurately represent the more color dense image, an arbitrary color can be assigned to each of the 256 available color 'slots' on the map. [...]

Concluding, 1 bit means that you can have only two states, e.g. black/white.