Clarification on Rayleigh scattering causing various sky colors (I know Rayleigh scattering isn't the only reason why the sky is blue but to simplify the question lets focus on that)
The commonly stated reason for why the sky is blue is that smaller wavelengths are scattered more easily off the molecules in the air. During the day, because the blue light is scattered more, the sky is illuminated more with that blue light and more reaches your eyes. However, during sunsets and sunrises, the light from the sun must travel a longer distance. The explanation I have found is that the blue light is scattered away and more of the longer wavelength reds and greens are available to reach your eyes to get those warmer colors, (red and green of course mixing to get yellows). 
My question is that it seems like these explanations are conflicting. If the light at sunsets and sunrises travels more distance, why won't the blue light be scattered even more and thus illuminate the sky with blue light more than in the daylight? It confuses me that in one case the scattering of blue light causes the sky to be blue but then at sunset the scattering eliminates this color. Could I get some explanation on this?
 A: When the Sun is directly overhead, the light is going through about the equivalent of 8km of sea-level air, even though the atmosphere is roughly 50km high. 
When the Sun is just on the horizon, it’s 15 times as far to that 50km height, with approximately the same density profile:  there about 120km of sea-level-equivalent air, or about 15 times as much. 
A lot more blue-end light is scattered away at sunset, 15X, leaving a redder sun. 
Why don’t you see it, I.e. why isn’t the setting-sun sky bright?  It’s because the scattering isn’t near you. With the sun overhead, most of the scattering is a few km up, which sets the typical distance. At sun set, that same scattering happens 100’s of km away as the light slants in. Yes, that makes the sky blue, but not your sky: it gives the bright blue to people who still have the sun high in the sky. 
A: Scattering experiment of thin milk: Mix a small amount of milk with water in cubic glass container. In the dark, we use a flashlight to illuminate the liquid from one side of the container. On the other side, we can see that the light passing through is reddish. On the top of the container, we can see that the scattered light is blue. The color of the sky can be compared. The color at dawn and before sunset corresponds to the light passing through the milk, and the light observed during the day corresponds to the scattered light of milk.
