One of the things that strikes me most about trees and Ents is perhaps so obvious that we did not really discuss it in class: These are truly ancient things. The first line of the "Ent" section in Appendix F states that they are "The most ancient people surviving in the Third Age." Forests first started growing during the Spring of Arda and the ordering of Middle-earth by the Valar. Yavanna created the Two Trees to provide light to all of Middle-earth. Before the coming of the Firstborn, before the awakening of the Dwarves, there were trees and Ents.
The Ents, possibly more than any other characters in Lord of the Rings, have a very direct connection with the Valar and with Eru Iluvatar. Yavanna, fearing for the safety of the trees she holds dear, perceived these Ents in the very Song of Iluvatar. "Would that the trees might speak on behalf of all things that have roots, and punish those that wrong them!" Yavanna cried, and then summoned the spirits from afar that would become the Shepherds of the Trees.
Treebeard is probably vying with Tom Bombadil for the title of "Oldest character in Lord of the Rings," although as an Ent, Treebeard is closely tied to Iluvatar's Creation, whereas Tom Bombadil is...just Tom Bombadil. It is Treebeard's age, and perhaps this connection to the divine, that strikes the hobbits most upon their first meeting. Well, not just his age, but the fact that Treebeard had been a conscious being for so long holds Pippin in awe: "One felt as if there was an enormous well behind [his eyes], filled up with ages of memory and long, slow, steady thinking." It is interesting, too, that Tolkien felt he didn't "create" the Ents, but rather that he was "reporting" something rather "unconscious" (Letters, p. 212n.)
I would guess that this connection to the divine the Ents have is part of the reason we can't just write them off as "wild" or mere embodiments of Nature. Like the Green Knight, in spite of all appearances, these Ents are more civilized than wild. They are shepherds, after all.
In terms of why some people hate trees...I must admit, this seems like a fairly silly idea to me as well (since someone else started their post with this thought). Perhaps "hate" is just the wrong term, because I would agree that many people have an "extreme disregard and/or apathy towards" trees. But this just complicates the types of trees that live in Middle-earth, because Tolkien both gives them the means to "fight back," as it were, while at the same time almost justifying someone's hatred for them -- it makes more sense to hate the type of trees that will ensnare unsuspecting hobbits, or swallow hordes of orcs. But it also seems that these "scary" trees of Middle-earth act this way because they lived in lands inhabited far too long by Morgoth's shadow, so I suppose they can't really be blamed for their actions.
Well, in case you need more evidence for my "Ents-connected-to-the-divine" argument, reread the Treebeard chapter. First, Treebeard works some magic over vessels of water to create light in his ent-house: "he held his hands over them, and immediately they began to glow, one with a golden and the other with a rich green light." This is more "magical" by far than much of what the Elves do, at least, not to mention that these Ent-water-lights recall the Two Trees of Valinor. Also, there's the matter of Ent-speech itself, which is downright musical -- related to the Music of Creation, you might say. Although the words that Tolkien includes are part Elvish, part Entish, and sound like nonsense, there's no mistaking the connection to music. Treebeard's voice sounds "like a very deep wood-wind instrument," when he spoke of orcs he "made a deep rumbling noise like a discord on a great organ," and as he walked he "talked to himself in a long running stream of musical sounds."
Basically, Ents are ancient relics themselves, and some, like Treebeard, have been around since the beginning of Arda itself, they are direct manifestations of Iluvatar's thought and Song. This quality impresses itself upon all those who meet the Ents, who cannot help but feel awe, and probably some smallness in comparison -- they feel not only young compared to the Ents, but that there is something otherworldly or divine in their very beings.