I don't think Jackson understood LOTR--I agree with Christopher Tolkein's criticism of the movies, although I do personally enjoy them, and I don't think you're "wrong" for liking them. I'll explain my take:
As I am sure you are aware, Tolkein was a classic British academic, like James Herriot was in veterinary medicine. He had a fierce and deep fondness for England and all of the colonizers that contributed to the English identity and and nation via art, migration, and war, primarily focusing on the pagans, the Norse, the Danes, and the Germans (the "Saxon" in Anglo-Saxon is from areas very close to Germany, Belgium, and the Netherlands). If you ever read James Herriot's memoirs, you'll hear a lot of similar admiration for the distinct English sub-cultures and the unique dialects, practices, personalities, and looks they had based on their conquering ancestors and their subsequent evolution.
As C. Tolkein complained, Jackson turned the IP into an action-spectacle that glorified war and battle. This doesn't initially make sense as a criticism, given that the novels center around a a massive war, but more investigation clears the matter up. LOTR was not military-forward because Tolkein loved war and action, but because he understood that the English identity was first and foremost a martial creation by the competition of unique cultures with long traditions of mythology and fairy tales, and it would be foolish to examine and display those cultures without the addition of warfare. A massive, ongoing war was the most convenient and English way to present his created cultures and languages, and he took the concept of honor and fealty between sub-nations very seriously. The England of Tolkein's youth educated their children that way, too; the history of England was taught to children as a series of battles that bookended reigns by different nobles. (This is supported by the childhood school memories of other famous English authors like Orwell and Dahl.)
So LOTR is actually a sort of mythical folk ethnography of northwestern Europe, with a primary focus on a mythical England as its center. It is not a clean 1:1 map (you can't just say "Dwarves = Germans"), but there are extremely obvious parallels. Hobbits are like English country folk, Elves are Scandinavian roving royalty, the Rohan horsemen are like mixtures of Steppe raiders and northern Scots.
A good example of how Jackson failed to understand Tolkein's creation was through his treatment of the hobbits. In the novels, the hobbits are crafty, industrious folk, who have the same eccentricities as the intelligent and cultured (but also petty and simple-minded) denizens of Tolkein's English country. The hobbits in the text are an ancient culture who perform long feats of academic genealogy, farm, distill, and are well-read and "mature" as we might compare them to modern humans--Tolkein's joke is that despite acting as landholding businessmen, scholars, and tradesmen, the main foursome are considered immature as compared to other hobbits.
Jackson, on the other hand, treats them primarily as drunken, silly teenaged sideshow halflings. His portrayal is very funny and I am fond of it, but he completely misses the gravitas of the Shire as he lays it out in the Fellowship of the Ring. The novel-hobbits are a functioning proto-industrial agricultural civilization with their own myths, narratives, political factions, and warfare (just like the real-life residents of the English countryside), but the movie-hobbits are funny hillbillies with pretty architecture, with some exceptions like Bilbo.
This theme of "complex martial culture reduced to laughs and action scenes" is common through all three movies, and it stretches through all of the cultures that Jackson portrayed. I think the most egregious casualty is in Return of the King, when the noble chivalry, restrained capacity for violence, and scholarship of Faramir is replaced with a silly "temptation of an inferior man" plotline, which to me shows that Jackson lacked the ability to take Tolkein's ideas really seriously. If you don't believe me, watch the Faramir scenes in the movie, and then go back in the book and read them. Novel-Faramir is a paragon of virtue, an intelligent, shrewd, and principled man who refuses to compromise his principles for the glory of Gondor, but also remains loyal to his father, as would be expected of a son of means and nobility in a battle-tested patriarchal culture.
That said, I do enjoy the movies and I don't think you're wrong for liking them. Jackson did an excellent job with the art, music, geography, character relations, military scenes, heroism, and pacing. I simply don't think he understood the underlying soul of the novels.