It's difficult to really comprehend how bad Halo 4 is as a Halo game and, in many regards, as a game in general. These are the some of the key reasons why I think this:
UI - this was the first thing I noticed when I booted up Halo 4, and it was a sign of things to come. It is literally one of the worst UIs I have ever seen, and was drastically worse than the usual clean Halo UIs I was used to. This was particularly evident to me as I had come straight from Reach which had the best UI I have ever seen. Rather than everything being layed out and simple to use, 343 chose to layer everything on top of each other for no reason at all. It's extremely confusing and is frustrating as hell.
Singleplayer - The story was diabolical. This is coming from some who has read most of the halo books and has been immersed in the Halo universe for years. Nothing makes any sense at all - some thing about a didact? A librarian? I was just being jumped around different areas for no reason and did not have a clue what was going on. I didn't care about any of the one dimensional characters, and there was no tension at any point as I knew that, this being the start of a new trilogy, master chief was not in danger of dying.
Other aspects of the story didnt make sense either, such as how did the humans manage to build a humongous space ship (about 300 times the size of a normal ship) in just a few years after the end of the covenant war? This war had resulted in the near annihilation of humanity as well as most of their colonies. Even a good chunk of Earth had been glassed. But the UNSC make it their priority to spend all their money on a giant ship. They need to get their priorities straight.
Mission design - disapointment again I am afraid. Gone are the wide open areas that you could maneuver around, and replacing them are extremely linear segments. For a lot of the missions you just inexplicably jump through portals to take you to the next area, as if the level designers could not be bothered finding a way for you to go on foot or vehicle.
Weapons - All the forerunner weapons are just copies of the human weapons - they have a pistol, shotgun, rocket launcher, sniper, BR, assault rifle. Not much interesting at all.
Enemies - for most of the game you are fighting the forerunners, which are more annoying to fight than the flood. They are simply not fun to fight: the dogs swarm you and jump around, the flying jerks back off when you are shooting them, and the knights are just frustrating versions of Elites. I didn't feel anything when I was fighting them either, they were just there and I just had to kill them.
Overall the Singleplayer was a slog that I was happy to finish. There was nothing in it that made me care about anything I was doing. The final QTE battle, and its inherent restrictions on gameplay, capped off and reflected what was a pretty awful Halo 4 Singleplayer.
Multiplayer - put simply, Halo 4 no longer feels like Halo. I know reach gets a lot of criticism here, and I agree that it did deviate from the traditional halo model, but to me Reach was still recognisably Halo. It was still based (for the most part) on skill, teamwork, and map control.
Halo 4 was much closer to Call of Duty than it was Halo. You have custom loadouts, perks, weapon skins, killstreaks, and instant respawing. You would simply spawn, run around shooting, die and respawn again. You didn't position yourself to control the map or weapon spawns, I don't even think that maps were made with this in mind. The killstreaks and alternating weapon spawns added another layer of randomness. It was just a mess.
As others have said, the maps were pretty awful as well and there was not enough small maps.
I'm sure people not familiar with Halo may enjoy the multiplayer but, as demonstrated by the halo 4 multiplayer population, most halo fans sure didn't appreciate it. I have gone from some one who played Halo 3 and Reach religiously, and as some one heavily immersed in the Halo universe, to completely indifferent over the series. I have absolutely no interest in future titles and have no faith in 343 to redeem themselves. In fact my avatar picture comes from a conference in which they stated that they would further dumb down halo to make it more accessible to casuals and newcomers.
Sorry for the wall of text.