I enjoyed the game, but most of the criticisms I hear aren't wrong. There's some glitches and frame rate issues, controls are unwieldy (even for veterans of Team Ico games), puzzle design could be a lot clearer, the strict scripted events aren't always clear (for example, Dunkey's video above where he jumped when Trico wasn't "ready"), and Trico's AI isn't always reliable. I guess the reason why I liked it so much is that when it did work as intended, it pushed all the right buttons with me (and when it didn't, it was sometimes unintentionally hilarious. I fell off a running Trico's back in an endgame cutscene and the kid stood there staring as Trico ran and skidded to a stop). It's so uncommon to see non-pet-sim games with a primary focus on relationships with animals, and said animals not acting purely like a machine (comparing, LOZ's Epona to SOTC's Agro). Personal tastes, but I know not everyone shares it. It's a potential masterpiece that is unfortunately weighed down by stupid stuff that makes it super unlikable to people that can't tolerate it. Regardless of opinion, The Last Guardian teaches a lot of lessons about gaming today, including how we shouldn't underestimate the importance of performance and controls, realism doesn't always translate to good game design, etc (some positive things too, but I guess the two I listed are the most relevant).
I adored Trico (from his big doofy face, to his smooshy feathers, to his derpy brain), but at the same time I work with animals as part of my career as a veterinary technician (which is like a nurse for animals). If I got pissed off easily at an animal that didn't do what I wanted them to do, I wouldn't have lasted as long as I have lol.