This is a tough one. I've seen one other film from Chang-dong Lee, Secret Sunshine, which I liked quite a bit. The Metacritic score for Burning was 90/100 ("Universal acclaim"). It's # 116 on the They Shoot Pictures, Don't They list of the top 1000 films of the 21st century. And it came up recently in a comment from a friend I respect who called it "my favorite film last year -- and one of my favorite films of the 2000s" (hence, "by request", although he didn't specifically make a request).
But Burning mostly left me scratching my head.
It falls into a few categories I've invented over the years. There's the "It wasn't made for me" category, usually combined with "Director achieved their aims", resulting in a movie I don't much like but that I nonetheless respect. (The patron saint of these categories is Terrence Malick.) Perhaps a bigger reason I was left unsatisfied is less because of a category and more because of a taste preference (although I guess that falls under "not for me"). I don't often like ambiguity in a movie, especially when I think it is purposeful. I used to complain about this, but over time I've realized it's more about me than about the filmmaker. I never understand the byzantine plots of international spy thrillers, and am always asking my wife, "what just happened?" (She has her own version of this ... if a movie mostly ignores narrative thrust, she is likely to ask, "is this about anything?" But she never loses her place in a spy thriller.) With movies like that, I'm left to appreciate the action, or the acting, or anything that doesn't remind me I have no idea what is going on.
Chang-dong Lee is intent on ambiguity in Burning. In one interview, Lee used the words "ambiguity" or "ambiguous" 11 times. It comes as no surprise, then, that his film is filled with ambiguity. I love movies that are non-judgmental towards their very human characters (Sid and Nancy), and that's a form of ambiguity. But Lee's ambiguities are larger than simple characters ... in the interview, he says "I wanted ... to discuss the ambiguities of the world we live in and how there seems to be no answer to the questions that we have today". Lee is up to something, to be sure, which is why I'd categorize it as "Director achieved their aims" ... he wanted to discuss ambiguity in the world, and he did so by making an ambiguous film. But, as I said before, my brain doesn't work right for this kind of purposeful ambiguity. More often that not, I'm wondering, "what is this about" or "what is happening" or "is this entire movie made up in the head of the main character"? And that gets in the way of my appreciation for the film.
As I was watching, I was thinking about a favorite movie of mine, L'Avventura. In that movie, a group of upper-class people are on a yachting cruise when one seemingly key character disappears. Her friends try to find her, but they soon lose interest. Only two of them stick with the search, but ultimately they are hardly better than the others, eventually beginning an affair. One of Antonioni's points is that these people are so self-absorbed that the loss of their friend means little or nothing to them. The audience may wonder whatever happened to the missing woman, but like the characters, we push that question to the back burner ... it's not what makes the movie interesting.
A woman disappears in Burning, too. But here, one character really cares about her fate. In fact, he obsesses about it, and that obsession is crucial to the film. We never find out what happened to her, or even if she existed ... ambiguity. But Lee makes us care about what happens to her. When Antonioni decides not to explain his disappearing woman, he is commenting on the way the people in the film have forgotten her. But Lee, in focusing on the man's obsession, invites us to understand what has happened, and when he purposely skips that information in order to maintain his ambiguity, well, he achieved his aim of discussing the ambiguities of the world, by making an ambiguous picture ... and that's going to end up in my "not for me" category.
Despite everything I've said, there is plenty to like about Burning. The actors portraying the three main characters (Ah-in Yoo, Jong-seo Jun, and Yeun Sang-yeop) are wonderful. This was Jun's first movie, and it doesn't show ... she effectively shows us the complicated nature of her character. Yoo is masterful in showing the way his obsession gradually grows. Most notably, at least for American viewers, is Yuen as the most mysterious character of them all ... notable because we know him as Steven Yuen from The Walking Dead, mysterious because we learn so little about him, and Yuen's facial expressions suggest a self-satisfied knowledge, as if we don't know, but he knows everyone else.
I am going on and on about a movie that will appeal to many ... all those critical raves, not to mention that of my friend, are evidence of that. Even as I complain, I find myself wanting to watch it again, see if it makes more sense. So if, for instance, you are intrigued by a movie where a greenhouse may not be just a greenhouse but a metaphor for something else, where your interpretation of the meaning of those greenhouses is a key to the story and your reaction to it, and where that meaning will inevitable be ambiguous ... then you should check out Burning.