The first Halo was not generic. It was a trailblazer, a genre definer for its generation. Hell, if it hadn't been as popular as it was, it would probably be looked upon as one of the greatest accomplishments of the 128 bit consoles. But, no. It was loved by the mainstream, and spawned a franchise. So the same people who extoll the virtues of Goldeneye 64 also condemn Halo, even though, in the long run, Halo: CE did far more for console shooters and tried many more new things. By today's standards it can certainly be called generic, but only because so many of the unique aspects it pioneered have been copied so endlessly ever since.
The second Halo couldn't have been called generic at the time - it was still arguably the best of its kind when it was released - but it was the beginning of what would become the Halo strategy: minimal changes, no new innovation. However, it was a technically superior game to the first, it did attempt a couple of new things and, most importantly, it succeeded at online console play like nothing before it.
Halo 3 is where the accusations of genericism start to gain weight. Don't get me wrong, I'm sure it's a fine game - critics certainly seemed to like it - but it continued to lack new innovation. This was largely excused at the time because "omgnextgenhalo!". The trails blazed by Halo: CE were commonplace in shooters now. Halo 3 was, technically, proficient in all areas. It was almost certainly better than its immediate competition. But no one can argue that the series wasn't beginning to stagnate as early as its third entry.
Halo ODST is probably the most divisive of the lot, excluding Halo Wars. It attempted some new things, but the new things it attempted weren't any good. Everything else was the same as ever. The multiplayer offered nothing significantly new, the campaign was too short, it was dull, it should have been a $15 expansion for Halo 3.
And then there was Reach. A Halo game that added very little that was new, and the stuff that was new barely affected the unchanged gameplay at all. You might point out that Halo "has bright colours", but since when has graphical style excused stagnant gameplay? Of course, I suppose I can't criticise it too much, I mean, the thing sold like...well, like a Halo title. And yet, while nothing worth a damn has changed, it's still fun. A lot of fun, especially with friends.
Halo is a game series with five major titles released over almost a decade that has barely changed at all since the 2001 original. It is a game with a silent space marine protagonist who shoots aliens with big guns, and takes place in a universe where humanity is at war with an alien alliance. It is a game with regenerating shields, a two-weapon limit and run&gun gameplay.
Yes, it is generic. There is no argument here - it is the very best example of a generic shooter. If I wanted to show someone an example of a generic shooter, I would show them Halo.
That doesn't mean it isn't good.