Call of Duty eSports is looked down upon because it's not a true eSport. For the game to even be played competitively or at a competitive level, 1/4 to 1/3 of the game's contents need to be banned/removed.
In terms of viewership, CoD is very boring to watch compared to other eSports such as LoL, and most importantly CS:GO. There are very few "clutch" or "intense" moments compared to other games, and it hurts the viewing experience.
In terms of skill, the skill gap in CoD is incredibly low compared to other games. Think about this: in a first person shooter game there needs to be some sort of skill involved in the shooting part of the game. This is typically broken down into 2 main areas: kill time and the difficulty it took to get that kill. In CS:GO, you have a very low kill time but it is considerably difficult to get that kill, depending on the range. In Halo, the kill time is very high and it takes moderate skill to get that kill (having to keep the reticle on the players head whilst they're strafing, Gandhi hopping, etc.). In Call of Duty, the kill time is very low and it is very easy to get kills: almost all of the guns have little to no recoil, and if they do have recoil it can a.8 be altered with the foregrip attachment or *b. be easily controlled. If you have a first person shooter game where it takes little to no skill to shoot someone, you have a very watered-down experience compared to other games. Let me put it this way: In CS:GO, if you put GeT_RiGhT or kennyS (in my opinion, the 2 best players in the world) against the average or casual player in a 1v1 AK47/M4/AWP duel, the pro player would win 10 out of 10 times. In Halo, if you put LxthuL or Roy (again, in my opinion the 2 best Halo players in the world) in a 1v1 BR duel against the average or casual player, the pro would also win 10 out of 10 times. In Call of Duty, if you were to put Scump or Clayster in a 1v1 BAL/ASM1 duel against the average or casual player, there's a good to fair chance that the casual player would win 2 or 3, maybe even more times. We see this happen all the time when pro players stream Ranked/pubs. In a game where it's very hard to seperate the professionals from the casuals when it comes to the core of the game, shooting, you're naturally going to have a game that is looked down upon.
In terms of professionalism, Call of Duty is at the bottom of the barrel. Our "pros" are on Twitter 24/7 complaining, nagging, or whining about either something in the game, internet, host, or any other thing that tends to get brought up on that particular day. With the exception of a few players (MerK, Nadeshot, etc.) our pros tend to be late-teen to early-twenty year olds that tweet whatever comes to mind and get in flame/roast wars with each other on social media.
In my opinion, the most important reason is that it's a console game. There are alot of things that come with this. 1 we're prone to continuous yearly or bi-yearly releases, which we see evident in Call of Duty with a new release (by a different developer each year, mind you) every single year. 2 is the price point. Console games sell for $60 retail, whereas other PC games such as LoL and Dota are Free2Play, and CS:GO is only $15 but consistently will go on sale for ~ $6. This makes it easier for people to take the risk and buy the game, because if they don't like it they're not really out that much. 3 is availability/accessibility. Not everyone out there owns a PS3/4 or Xbox 360/One. However on the contrary, EVERYONE out there owns a PC in some form, whether it be desktop or laptop. This makes it extremely easy for people to download the game and play it anywhere and everywhere, assuming that location has WiFi (which we all know nowadays is everywhere.)
These are just a few of the important issues with what's wrong with CoD eSports. There are many others such as the lack of dev support, MLG.tv stranglehold, and many others, but I've typed plenty already (and I also have to leave for class in 3 minutes).