I admit: I never entirely drank the Karl Lagerfeld Kool-Aid. I was not one of those critics (and there were some) who would clutch their breast, shriek “genius!” and swoon after every show.

I often felt that for every extraordinary piece the designer created for Chanel or Fendi — by the time I started in fashion, his career at Chloé was at an end — there would be another clunker of a dress or a suit: unflattering, frumpy, kind of awkward. I found the set-building he did for his Chanel shows in the latter years (the supermarkets, rocket ships and icebergs in the Grand Palais) not just a smart social media move (which it was) but too often an egregious display of a bottomless budget and sleight of hand to distract from what was on the runway. Sure, that tweed sweatsuit made that model look like a Real Housewife — but everyone was looking at the double-C branded pasta on the faux megamart shelf instead!

Once I got spoken to by the Chanel press office for not fully “understanding” Lagerfeld’s vision. But as I wrote in the designer’s obituary (he died in 2019), while he unquestionably changed the business of the industry — its marketing, its branding, its very structure — thanks to his ability to take on a heritage house like Chanel and reinvent it with the detritus of its own codes, I didn’t think he really changed wardrobes. He didn’t give the world a new silhouette, or an expression of identity, the way Coco Chanel herself did, with the bouclé suit, or Christian Dior, with the New Look, or Saint Laurent, with Le Smoking, the tuxedo suit for women.

All of which is to say that when I heard the Metropolitan Museum of Art would be dedicating its 2023 Costume Institute show to Lagerfeld, I had a mixed reaction. On one hand it made sense: In a 65-year career, which included 26 years at Chanel, 54 at Fendi, 25 at Chloé (in two separate stints), and 35 at his own brand (for years he juggled multiple jobs at the same time), plus stints at Patou and Balmain (phew), the man loomed like a colossus over the modern fashion landscape. On the other hand, the show raised a lot of questions.

The bar is very high for one-person exhibitions — usually defined by names that changed the vocabulary of dress. There have only been 10 of them at the Met in the last 50 years, including Balenciaga, Saint Laurent, Alexander McQueen and most recently, Rei Kawakubo of Comme des Garçons. Generally, the Costume Institute has focused on thematic displays, like last year’s show on American fashion, or 2019’s “Camp.” And even beyond the questions of Lagerfeld’s actual products, there were the issues of his public statements, a number of which were fatphobic, Islamophobic, racist and sexist, deriding everyone from Angela Merkel, the former chancellor of Germany, to the singer Adele.

Should he really be put on a museum pedestal, his art (if that is what it was) separated from his self?

An answer of sorts can now be found in “Karl Lagerfeld: A Line of Beauty,” which opens May 5 in the museum’s Tisch Galleries. It is a tightly edited, highly enjoyable, ultimately convincing argument from the Costume Institute’s curator in charge, Andrew Bolton, that when you strip away the controversies and the mythology, what you are left with is a pure expression of a great technical imagination combined with an omnivorous cultural curiosity. The advantage of 65 years of work that produced over 10,000 pieces of clothing (at least that’s the number Bolton said he perused for the show) is that in distilling them down to just over 200 garments, Bolton is free to focus on the most evocative pieces. And they are almost all, indeed, dazzling.

But the exhibition also fails entirely, and deliberately, to address the complications of the man. Bolton admits as much in the introduction to the exhibition’s catalog. “We did not want to emphasize ‘Lagerfeld the man,’” he writes, but rather “Lagerfeld the designer”; to find the connective tissue in a 65-year career that could often seem profligate in the extreme: flitting here, there and everywhere; reluctant to commit. In an interview this week, the curator elaborated on his stance, saying he wanted to leave the judgments on character to historians and biographers. And yet Lagerfeld the man is also the ghost in the machine of the show: impossible to ignore.

Indeed, the concept around which the exhibition itself is built — a narrative of dualities — implies the paradox at the heart of the Lagerfeld story: He was a man who loved, and made, beautiful things while sometimes blithely giving voice to ugliness.

If not officially a retrospective — Lagerfeld famously hated them, saying no one wanted to “look at a bunch of old dresses” — the show is more like an essay in clothes, based on an organizing principle derived from the 18th-century artist and writer William Hogarth’s 1753 book “The Analysis of Beauty,” with the author’s beloved Serpentine curve, or “line of beauty,” which signified liveliness and variety, juxtaposed against the straight line, which Lagerfeld also prized, as the dueling forces in his aesthetic. (“The Line of Beauty” is also, as it happens, a 2004 Booker Prize-winning novel by the British writer Alan Hollinghurst about gay life, class and politics in Thatcherite Britain, but though Bolton acknowledged that he loved the book, he said it had nothing to do with the exhibition.)

From there the lines and dualities proliferate in nine different groupings: the masculine/feminine lines giving way to the romantic/military influences, which give way to the rococo/classical, which in turn lead to the historical/futuristic and so on and on. There are so many lines they can be hard to follow; Bolton has a tendency to over-egg his theses, perhaps to justify fashion’s place in the museum. In the end you can ignore them all, and enjoy the show purely as a visual feast.

The line conceit proves most useful in providing a template for the show’s designer, the architect Tadao Ando (who was once commissioned to create a house for Lagerfeld that was never built). The space is composed of multiple galleries that undulate and curve around on themselves with little openings through which other galleries can be glimpsed — to allow peeks forward into the future, or back to the past. The effect is slightly disorienting in a good way, making it easy to lose oneself in the fields of Lagerfeldiana.

And what fields they are. Two little tweed Chanel lunching suits seem to vaporize into mist at the hems. An egg-shaped Fendi coat is composed of thousands of tiny brightly colored mink mosaic tiles, like a pointillist painting; another, strafed by overlapping shades made of layers of scrunched-up tulle that only look like fur. Lagerfeld could see possibilities in material that seemed otherwise inconceivable; he minted sequins out of concrete, and wood.

There are Chloé dresses in Sonia Delaunay-esque prints and trompe l’oeil Grecian drapes. A Chanel frock coat is cut away not at the front but at the back, to expose frothing iridescent tiers. There are almost no logos in sight (a fun game is: guess which look goes with which brand; all three of his main employers were show sponsors), just as there is little of the kitschy play with brand iconography that helped make Chanel a part of pop culture — the double-C boxing gloves, and bikinis — and that has been widely imitated at other brands. But there are cumulus clouds of feathers and blossoming rosettes made of lace and gleaming sequin armor that romp across centuries and salons.

Through it all, one shape appears again and again: the jacket pinched just a bit at the spine, so the shoulder blades roll up and back, raising the arm hole just so, with the line curving down over the waist. Bolton calls this the “Schlemmer shape,” after an Oskar Schlemmer painting, “Bauhaus Stairway” from 1932 (the period between the wars in Germany having been one of Lagerfeld’s gravitational poles).

Ditto the sketches that were Lagerfeld’s primary means of communication, and are displayed with garments as their origin story. The designer would hand these drawings, which were conceived in the round (he thought not just from the front, but from the back) to the heads of his ateliers, to be “read” like their own private language. Just how that worked is enlivened by a group of absorbing videos created by the documentary filmmaker Loïc Prigent that are interviews with those premières d’atelier — the people who translated the designer’s sketches — about their work with Lagerfeld. They exude humanity, affection and pride.

As it happens, the videos are shown in the exhibition’s first gallery. You reach them after an entrance antechamber with another video, this one a close-up of Lagerfeld’s hands sketching a dress, along one wall; at the end of the room, like a punctuation mark, is a reconstruction of Lagerfeld’s Chanel desk, piled high with books and papers (each element chosen by Bolton to represent the breadth of Lagerfeld’s various obsessions, from Aubrey Beardsley to Diet Coke). Next to the desk is a pair of the designer’s black shoes, sitting empty on the floor. This opening video and desk mirror the exhibition’s close: another video of Lagerfeld’s hands, sketching — this time not dresses, but himself. Catty-corner to that visual are a set of vitrines displaying the designer’s signature accessories: the fingerless black leather gloves, black shades and fan, that were the artifacts of the character he constructed for himself. Or “caricature,” as he called it.

Just before that, however, is a small ellipse of a room lined with 80 iPhones plus one at the center, all loaded with the same video of Lagerfeld laughing, as well as some of his most famous quotes: “I have one instinct that is stronger than all others: the survival instinct”; “I always say what I think, and sometimes even what I don’t.” None of the bad ones, of course, though the latter statement seems particularly telling.

It’s a lost opportunity. Because by choosing to sandwich the clothes between representations of the man, the show actually suggests you can’t separate that man, in all his messy, uncomfortable reality, from the alchemy of his art — and you shouldn’t. That mess and discomfort is part of the mix; it’s part of the legacy, as it is for many of our most formative figures. If the Met can’t encourage that public conversation, what institution can?

Lagerfeld once said, in a quote that is inscribed over the entrance to the show, “Fashion does not belong in a museum.” This exhibition makes a glorious case that the clothes he made really do. But so, too, do the complications, and the tension.

Karl Lagerfeld: A Line of Beauty

May 5 through July 16, Metropolitan Museum of Art, 1000 Fifth Avenue, Manhattan; 212-535-7710; metmuseum.org.