Gotta Dance! (No, seriously, there IS a reason!)

There is one truth about old movies that science has yet to explain:  If you want to convert one stubborn unbeliever to vintage films, show them 1952's Singin' in the Rain.  You could show them Gone with the Wind, or The Maltese Falcon, or Double Indemnity, or anything else off the AFI 100 list, but for some reason, Singin' is the one with the highest instant conversion record.  It just works, with uncanny mind-enslaving skill.

It's not hard to theorize why--Under Stanley Donen's characteristically playful direction, the script was by "On the Town"'s team of Betty Comden and Adolph Green, and like most of Comden & Green's scripts (The Band Wagon, It's Always Fair Weather), there's a healthy dose of snarky fun poked at the phoniness of the show-biz industry, and characters who aren't quite what they've fraudulently cracked themselves up to be:
The movie opens with a comically garish over-the-top satire on 1920's Hollywood red-carpet premieres, into a montage where Gene Kelly, as silent Hollywood's biggest Cheshire-grinning insincere matinee-idol star, gives his fans a somewhat, er, embellished story of his rise to stardom ("Dignity...Always dignity") as we see his version clash onscreen with the less-dignified truth.  And along the way leads into the "Fit as a Fiddle" number where Kelly and Donald O'Connor as corny vaudeville performers turn song-and-dance-man tap into synchronized athletics.
That's the first eight minutes, folks.  Count 'em.  Ninety-five to go, and it's got even more surprises up its sleeves from there.

Singin's unquestionably one of the great ones off the Great lists, but it still doesn't answer the question:  Why always THAT one?
Think it may have more to do with the audience than the film itself--Most first-timers don't expect to be quite so, well...blitzed with a sudden attack of almost contemporary humor, followed by Kelly and O'Connor's creative tapping that wasn't quite Fred & Ginger in top hat and tails.  It usually comes as a complete surprise to them to find a musical with that much story to its story, with the silent-parody plot...And frankly, may not have expected that much humor, as they may not have been expecting humor in an old MGM musical at all.  It's rather like the fear you may have had being forced to read Great Books in high school and freshman class, before discovering they had enough of an actual story to make a Great book a good one....Well, what did you think was on all those pages?

Although I had less personal success converting my own dad, who didn't know ahead of time what the movie was about, or all the classic-clip fuss was about either.  To get him to watch, I explained the plot of Jean Hagen's Oscar-nominated comic antagonist and the wiseguy silent-Hollywood satire, but his cold-feet curiosity still couldn't get past the one question:  "Yeah, but why was Kelly singing in the rain?"  Um, he was happy, I had to answer, he'd just realized he liked Debbie Reynolds.  (The gimmick was that the songs in Singin' were all reimagining pre-existing Arthur Freed and Nacio Brown song hits from the 20's out of context, and when Kelly imagined a scene for the title number, he told now-producer Freed, "It'll be raining, and...I'll be singing.")

When MGM's 1974's compilation-film "That's Entertainment" came out of nowhere to be one of the surprise box-office smashes of the troubled Ford-administration era--with a tagline distinctly historical to its time--it created two things:  One, it created a mania in our culture for reappraising the "late show" movies of the 30's, 40's and 50's, and a trendy fascination about the "Old Hollywood" that was facing destruction in '73-'74--From back in the days when, presumably, stars were more elegant, movies more watchable, and more of them were made on schedule to fill big velvet-seated theaters.  The second--since the focus had been on MGM musicals--was that it created a backlash of parodying Old-Hollywood era musicals and sanitized Hays Code-era movies as being just too danged happy and virginal to live in the troubled days of energy crises, inflation, political coverups and the sexual revolution, and popularized a social criticism of Depression and wartime people "escaping their troubles" at optimistic movies...Idiots.  And heaven help the early-50's movies, from the days of Betty Crocker housewives and duck-and-cover.
One reason for the latter, was that being a compilation retrospective, "That's" did not show the whole films in context with the original films they came from--It just showed the Good Bits.  And speaking from my own experience at least...Good Bits can be a bit confusing to the uninitiated.  What was created was the confused belief by the public that musicals of their parents' day must have apparently been nothing BUT strange overproduced production numbers thrown at a cringing audience, like the Ziegfeld Follies or a 70's TV variety show.

Some current generations may dismiss most of the old classic 20th-century catalogue (or at least anything made before the Big 80's) as "toothless", but if you're afraid to watch, don't worry, they won't bite--There's a context for everything, and it just takes a little bit of subplot to tie it together.  Everything happens for a reason, and it's usually sure to tie itself up by the climax.  That's how Hollywood worked back then, when there were studio moguls to make sure it did.
For an experiment, let's take THE most demonized, parodied, ridiculed, icon-referenced, giggled-at and generally straw-man-symbol persecuted scene in MGM musical history:  Esther Williams' "smoke" number (it wasn't a specific song) from 1952's Million Dollar Mermaid.

Isn't it silly looking?...Everyone's so HAPPY!  The Technicolor is crazy!  All smiles, all happy, and no one's makeup is wet and sparklers don't extinguish, through the miracle of reversed footage. I mean, making movies around a pool just for a swimming star to swim in?--Why, that's as nutty as the time they made movies around an ice rink just for a skating star to skate in!
The closeups of smiling extras, forming those kaleidoscopic patterns with their perfect legs, seems to be held up as the most instantly recognizable icons of all the artistic "excesses" of Busby Berkeley musicals..Despite the fact that Berkeley did not direct the movie, Mervyn LeRoy did (Berkeley was only hired as "Musical number designer", and it's considered that MGM held back his more insane/abstract visual ideas compared to Warner and Fox), and only two or three musical numbers appear in the entire movie, all as "onstage" productions.
Among other parodies of the number over the years--by everybody from the Village People to The Muppets--the most recent was in Joel & Ethan Coen's 2016 "Hail Caesar", where Scarlett Johansson as the faux-Williams actress on set has to cut the number's take short before her high dive because of a sudden gas attack...Yuk yuk.  And then a set assistant has to remove the actress's tight-fitting rubber mermaid-tail, with audible "pop"...Oh, my sainted aunt's sides.  Nothing's more rollicking than somebody with issues.

So, what fresh flippin' Technicolor heck IS going on in the number?  Well, that might involve seeing the other 105 minutes of the movie:

The story of "Million Dollar Mermaid" is a straightforward Hollywood showbiz bio of marathon swimmer Annette Kellerman, "the Australian Mermaid"--who first popularized one-piece sport swimsuits into fashion--who went on to invent the water ballet as a star of New York's Hippodrome in the 1900's.
Yeah, but why's she coming out of the pool with sparklers?  And what's with the trapezes?  And the guys in thongs? Um...it's supposed to be one of the shows she did.  At the theater, 'n stuff.  Albeit embroidered upon with a bit of Busby Berkeley license, to liven things up for the movie audience a bit.
(For the record, the real Kellerman wore a mermaid tail in many of her stage ballets and silent films, but Williams in the two hours of "Mermaid" does not.  Kellerman's tail costume was relatively loose-fitting, so neither one had to worry about gas.) 
If it's any consolation to realist cynics, the movie even ends on a relatively un-happy note, with the on-set accident that occurred during filming of Kellerman's 1914 "Neptune's Daughter"--And worse yet, with Williams' Kellerman happily marrying Victor Mature's character, who's been shown to be thoroughly reprehensible up to this point and only lucked into his own real-life fame as a show promoter by accident.  The real Kellerman, btw, didn't think much of Hollywood's version either.

See how it works?:  The goofy stuff is a little more complicated now.   Attaching a plot to an old movie is like newspapers giving a face and a name to a crime victim--A symbol is now a person.  A statistic is now a story.
And in the case of movies, there are a lot of stories, since most of them had to fill the remaining 90 minutes or two hours past the one or two minutes or so that compilations and retrospectives may have forced down your throat.
It's the first tease you learn when you open the Pandora's-box of vintage classics:  The movie you THINK you know, you probably don't.

And it's the first truth in the curiosity that leads to learning, that You Wouldn't Believe What You Don't Know.