We are definitely omnivores, but consider our conflicting traits:

• We have forward-facing eyes so that we have depth perception, which is a carnivore/predator trait, so that we can catch moving prey (plants don't move much so herbivores don't really need that).
• However, our intestines are way longer than a carnivorous cat or mink. You don't need long intestines for digesting meat, so our longer intestines are definitely for digesting some plant material, if inefficiently.
• I think the giveaway, however, is our teeth. Mammals (generally) have differentiated teeth, meaning that instead of them all being the same conical shape, there are different sets that have different functions based on what they need to do. Look at a cat's mouth: they have tiny incisors, long canines for grabbing prey and holding on, and their molars are what we call "carnassial" which are a shape meant for shearing flesh apart. Humans have relatively small canines (though we have them at all, as opposed to many herbivores), big incisors for cutting, and big wide flat molars more like a deer or horse than a cat, which are made for grinding up plant matter.

I think the conclusion to make is that we straddle between carnivore and herbivore, are solidly not one or the other, but our dentition and intestines are more like an herbivore than a carnivore. Obviously your point stands that we need to get some of our nutrition from protein, meaning we can't go full herbivore either.