why do so many people enjoy the call of duty series

[Mummelmann]

The two first ones are by far the best in the series imo, so I think you're missing out.
There are a few reasons why I like Call of Duty, especially the two first ones.
I remember playing it for the first time, I was shocked at the pacing and setting, there was literally no time or room to breathe, you just run for your life, find cover and shoot down as many enemies as you possibly can.
It was probably the first shooter I had to lay down suppressing fire while running for cover so I wouldn't die and that instilled a tremendous feeling of danger and excitement in me!
Another great aspect of the series is the team AI, not that its very good or anything (in the first one, your teammates were notorious for running into a building that the enemy had just tossed a grenade into, getting themselves killed by practically running towards it instead of away from) but the whole sense of having the team, their personality and intensity of some of the firefights due to the high number of enemies.
Before Call of Duty, most shooters were of the kind where you ran alone, with 8-10 different weapons and near infinite amounts of ammo and you encountered dumb enemies in narrow hallways and corridors, gun them down without wincing and move on.
Rinse and repeat, there were no tactics or real objective to anything, really.

Another part where the series excels is variation, you drive different vehicles, shoot from planes and generally encounter a vast lot of different weapons, terrain and situations and that lends the feeling of never knowing exactly what's going to happen next (the exception to this is World at War, it lacked these elements and had other huge issues so I don't see any reason to like that games at all, in fact; I hate it).
The sounds, the dramatic music pieces, the effects of artillery shelling, grenades and overall chaos of the battlefield is awesome and sublimely put together.
Many people think that playing a game where you can easily die is boring, they want to be in control and set the pace of the game themselves but CoD is all about hanging from a 12.7 on the roof of a Hummer trying desperately (and failing) to shoot any and all enemies who are doing their darnedest to blow you up.

Such is war, such is Call of Duty. It decides whether you live or die, not in the most realistic fashion but it feels great and frustrating all at once (as opposed to just frustrating as in Brothers in Arms).
And these are some of the reasons why I love this series!