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Explain why 0 degrees longitude and 180 degrees longitude are not designated east or west?

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0 degrees longitude does not have a designation of east or west because it behaves like a mathematical zero. It is neither positive nor negative. It is simply the start. Longitudes run through the north and south poles. Therefore, 0 degrees longitude is actually on the same line of longitude on the other side of the world which is 180 degrees longitude. Since all the longitude lines work like this, 180 degrees is the highest degree of longitude that you can have. Here is where it behaves just like 0 degrees because it cannot be any larger than 180 degrees. There is no need to say whether it is east or west then.
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What is the line of longitude at 0 degrees?

The line of 0° longitude is called the prime meridian (it is also known as the Greenwich Meridian).
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Why is 0 degrees and 180 degrees not designated east or west?

Simply because it doesn't matter in either case. -- Zero east or zero west puts you on the Prime Meridian either way. (Beginning on the Prime Meridian, you may travel 0° (MORE)