What I mean is that is it more dangerous than other contact sports that aren't martial arts? Such as Football, Soccer, Basketball, etc...
And if yes, why?
I'm not sure that your statement about the safety of boxing is generally accepted.
Boxing advocates point out that amateur boxing has fewer injuries than soccer, gymnastics, etc. However that source doesn't cite how they measure "fewer injuries", and doesn't state whether they count long term damage to the brain. There is some evidence that even amateur boxing can cause brain damage.
Ultimately, you may want to look at a source which compares injury rates. A quick google search suggests that football and soccer have the highest injury rate/hour practiced. But that doesn't address the severity or long term consequences of those injuries.
At a good gym, meaning experienced coaches and decent equipment, boxing/kick-boxing should not be that dangerous. First of all, you're probably not sparring right away, and once you are its in a controlled environment with mouthpieces, headgear, gloves, and shinpads(if kickboxing).
As pointed out in a previous answer, you are probably at an increased risk of facial bruises, bloody noses, etc, but not serious injury. However, if you are training for an MMA style of fighting which includes takedowns, your rate of injury is going to spike sharply.
Comparing it to other sports is tricky. Even at a high-school level we certainly had a higher level of general injuries in football, and typically more severe...broken bones not being uncommon. Basketball didn't have the same high incidence of really violent injuries, but a much higher incidence of high ankle sprains and the like. Soccer seemed relatively safe but I never played at a highly competitive level, and if you watch the Europeans play you'd think it was more dangerous than trying to snuff volcanoes with your bare hands with the frequency they go down screaming in pain.
In short, I think there are too many variables to objectively answer your question, but the above has been my (anecdotal) experience.
The short answer is yes. The very point of the sport is to do damage to your opponent. That being said, the chances of you actually breaking something (apart from your nose) is pretty rare. The only particularly dangerous thing that can happen to you in boxing or kickboxing is a concussion, which can and probably will cause scarring of the brain and make you "punch drunk" after a few years.
So yes, boxing and kickboxing is pretty dangerous, but the types of serious injury is limited to your brain unless you're very unlucky.
TL;DR: Yes, kickboxing, MMA, and boxing are extremely dangerous.
The greatest risk in all combat sports in which blows to the head are allowed is traumatic brain injury. When it comes to traumatic brain injury, boxing is by far the most dangerous sport, but kickboxing and MMA aren't far behind.
From an article on a 2014 study, limited to kickboxers and MMA fighters:
From an article about an ongoing long-term study of brain injuries in boxing and MMA, whose results to date were published in 2015:
Why are boxing, kickboxing, and MMA more dangerous than non-combat sports?
TL;DR: Because in team sports, blows to the head are an unfortunate but inevitable consequence of the game; in combat sports, blows to the head are one of the goals of the game.
American Football, Basketball, and Soccer:
In American football, you're trying to get the ball into the end zone and stop the other team from doing likewise. In basketball, you're trying to throw the ball through the hoop and stop the other team from doing likewise. In soccer, you're trying to kick the ball into the goal and stop the other team from doing likewise. Someone might get hurt in any of these sports, but that's a side effect, not the primary objective.
In boxing, you're trying to punch the other guy until he is unconscious or unable to fight; although body shots sometimes achieve this goal, the surest way to pull it off is to punch your opponent in the face and head as many times as possible, as hard as you can. In other words, you're basically doing everything in your power to give the guy a concussion. What is a concussion? Simple: a concussion is traumatic brain injury. Thus, when two boxers step in the ring, they are essentially trying their hardest to inflict traumatic brain injury on one another.
The fact that boxers are restricted to hitting each other from the belt up increases the rates of brain injury, because you are only allowed to hit opponents on the end of the body where the head happens to be.
Aside from brain trauma, the most common injuries in boxing are broken bones (usually in the head and face - noses, eye sockets, cheekbones, jaws - but sometimes in other places - especially the ribs and hands), eye damage, and swelling. These are relatively minor, relative to brain injury, and easy to overcome.
In kickboxing, as in boxing, the goal is to hit your opponent until he is unconscious or incapable of fighting; however, you're allowed to strike with more of your body (hands, feet, shins, knees, and elbows, as opposed to just your hands), and you're allowed to hit the opponent in more places on his body (basically, everything except the testicles, throat, and eyes, as opposed to only the face, sides of the head, and front and sides of the torso).
This simultaneously reduces the percentage of shots that will be delivered to the head (because more areas are fair game) and increases the kinds of shots that will be delivered to the head (because you're kicking AND punching, and because punches can strike with other parts of your hand, not just your knuckles). It also helps that you can block incoming attacks with your legs as well as your hands and arms.
All in all, kickboxing is slightly less likely to cause brain damage than boxing is, for all the reasons mentioned above, but the difference is negligible.
However, other injuries are far more common in kickboxing than in boxing, mainly broken bones in the arms, legs, feet, hands, ribs, and face. And obviously, there's plenty of bruising, and some damage to ligaments and tendons.
If kickboxing can be described (via a slight oversimplification) as "boxing plus kicking", then MMA might be described as "kickboxing plus grappling". All of the factors I mentioned in relation to kickboxing apply here, but there is the added component of the grappling: whereas boxers and kickboxers are limited to striking, MMA fighters have other options. They can grab, hold, throw, wrestle, etc.
Obviously, the grappling angle of MMA means that even less time is spent trading shots to the face and head than is the case in kickboxing; as a result, traumatic brain injury is probably slightly less common in MMA than kickboxing, and even less common than it is in boxing. Again, though, the difference is relatively small.
On the other hand, some researchers believe that MMA might be a bigger risk for brain injury, although their findings were based on reviewing fight tapes rather than examining fighters or their medical records. They speculate that one reason for MMA being more dangerous is related to the fact that MMA bouts often end with the dominant fighter delivering a flurry of head shots to his opponent, while the opponent is pinned on the ground and incapable of defending himself.
Non-brain-related injuries are probably more common in MMA than in kickboxing or boxing, and in addition to broken bones, bruising, and torn ligaments/tendons, dislocations are more common because of grappling and submission holds.
If you're still not convinced, you might want to look at the Manuel Velazquez Boxing Fatality Collection, which lists all the known, recorded cases in which boxers died due to injuries sustained in the ring. At present, the raw data lists 2,045 such cases between September 1724 and December 2015; there are 1,324 boxing deaths listed between December 1915 and December 2015.
There is no such resource for kickboxing or MMA, and I'm not aware of any similar resources for any team sports.
While black eyes and minor bruises or the occasional broke nose are quite common in boxing, i think the devastating injuries like cruciate-ruptures are rare.
From my non-representative experience i'd say that runners, soccer-players and the like usually spend more time with doctors because of knee-injuries or broken ankles than (thai) boxers.
Boxing happens in a very controlled environment, there is only one opponent to pay attention to and the attacks and defenses are well-established. While there is a big strategic component, there is not much creativity going into making up moves on the fly.
Soccer for example seems much less predictable to me. While running at full speed an focusing on the ball one may have to deal with being tackled at any moment.