Why are you complaining? What special advantage do you think you’re entitled to? This American slang expression dates from the first half of the twentieth century and became popular in the armed forces during World War II, in reply to any kind of griping. The actual addition of an egg to a glass of beer is presumably viewed as some kind of enrichment; one writer suggests it was regarded as an aphrodisiac, enhancing potency. The traditional English wassail bowl contains porter, eggs, and sherry, and Thomas Hardy (in The Three Strangers, 1883) gives a recipe for mead that includes egg white, but few if any other recipes call for such a combination, and probably they have nothing to do with this cliché anyway.