What is the reason for this?
At least in The New York Times Manual of Style and Usage (1999), the generation names are indeed treated inconsistently:
baby boom. As allusions to the population surge after World War II—between 1946 and 1964—baby boom and baby boomer are overused; ration them.
Generation X. The term for people born in the 1960's and 1970's. Also: Gen X; Gen Xer(s). All of the terms are faddish, and the short forms are slang as well.
Somewhat similarly, The Associated Press Stylebook (2002) has this for baby boomer:
baby boomer. Lowercase, no hyphen.
The 2002 edition of this style guide doesn't address Generation X at all, but I'm fairly sure that more-recent editions recommend initial-capping the term.
Why the inconsistency? I think several factors are relevant. One is timing: According to Merriam-Webster's Eleventh Collegiate Dictionary (2003), baby boom was coined in 1941 whereas Generation X first appeared in 1989:
baby boom n (1941) : a marked rise in birthrate (as in the U.S. immediately following the end of World War II) — baby boomer n
Generation X n (1989) : the generation of American born in the 1960s and 1970s — Generation Xer n
MW's first-occurrence dates make clear that the generational terms arose decades apart, in very different contexts. Since baby boom first appeared five years before the World war II ended, it clearly did not start its life as a generation name. When observers did recognize the postwar increase in birthrate as a significant phenomenon, their focus was initially on the increase itself—not on the cohort of human beings born during the first years of it. And by the time observers adopted the generational name baby boom/baby boomers for children born between 1946 and 1964, the lowercase style for the terms was well established. I note, too, that William Benet, The Reader's Encyclopedia, second edition (1965), spells the term lost generation—used in reference to "the generation of men and women who came to maturity during World War I (1914–1918)"—in lowercase.
Generation X, on the other hand, came into the world as a generation label, if we may trust the Eleventh Collegiate. That's not strictly true, of course, since Billy Idol's poppy-punky band Generation X debuted in 1976—but Billy Idol was born in 1955, so he was a Baby Boomer, not a Gen Xer, except when he was on stage. It's also true that generation X has long been used as a designation for first-generation populations in (for example) animal breeding operations or genetic experiments with Drosophila fruit flies. Thus, Glen Black, American Beagling (1949) [combined snippets] has this description:
However, the tendencies will certainly follow those laws of Mendel to the extent that these two sizes [of Beagles] are available without offsize ancestry, and the Beagle breeder can always aim his operations so as to be more certain of the size of the offspring from generation to generation.
For the sake of illustration let us assume that truebred large and truebred small Beagles were available for breeding in the foundation generation. Then the size could be definitely controlled within certain limits as illustrated in the accompanying pedigree. Starting breeding operations with foundation generation "X," the succeeding generations are numbered in parentheses consecutively:
I always assumed that, in naming his band Generation X, Billy Idol was comparing his generational cohort to a hatching of fruit flies in a controlled experiment. In any case, I don't find it at all implausible that the generational designation Generation X may have been influenced by the prior existence of the catchy band name—which was already a proper name.
Another element at work here, I suspect, is style-guide inertia. The point of a house style guide (like the New York Times's) is to ensure that the publication's way of handling particular troublesome terms remains consistent from one issue or volume to the next. Bu this introduces an inertial drag on existing style decisions—so even when a new term comes along whose treatment seems to be inconsistent with the treatment of the older term, the older term's style may not change.
A peek at the fifth edition of The New York Times Manual of Style and Usage (2015) indicates that the newspaper's current style calls for baby boomer, Generation X, Generation Y, and millennial as generational references. Not surprisingly, other publishers disagree, which is why you'll sometimes see every generation name initial-capped. In my view, the underlying absurdity of carving out supposedly meaningful generational blocks on the basis of arbitrary criteria is made no more absurd by the act of formalizing those designations with initial caps. But others may feel otherwise.
The term 'Generation X' was created from the title of the novel 'Generation X: Tales for an Accelerated Culture'.
Since the title was capitalized, the term when used to refer to the generation is capitalized, not because it is always referencing the book but out of habit starting with the title.
I don't think there's a hard-and-fast rule that says "Baby Boomers" is not capitalized. I would capitalize that expression. Here's a sample from the web -- a social marketing resource for library professionals, no less -- who also capitalizes this phrase:
BabyBoomers.com also seems to approve of the capitalized version:
And if CNN can be trusted, they also seem to prefer the capitalized version:
The term "baby boom" was first used in the lower case to describe the demographic phenomenon. Only later did it "cross over" to describe the generation that resulted from this phenomenon. Therefore, it retained its original case structure.
The term "Generation X" was "born" as a descriptor of a generation. That's why it was capitalized.
William Strauss and Neil Howe who literally wrote the book on "Generations" suggest shortening "baby boom" to "Boom" (and capitalizing it).