Is swimming bad for you because there is a risk of drowning?
If you push somebody in a pool who has no idea how to swim, bad things happen.
Likewise, push somebody into Crossfit box who is ill-prepared and bad things happen. That gets amplified when you have unqualified coaches (the overwhelming majority of Crossfit Boxes right now).
The definitive answer is that Crossfit can be bad for you at certain boxes under certain context and might otherwise be quite good for you at other boxes (especially if the alternative is doing nothing or training with bad habits), all depending on your current level of skill.
The danger in almost anything is associated with the context. In the context of Crossfit, if you are ill-prepared for the demands of Crossfit (and the majority of people are) then it is most likely bad for you. If you're generally already quite fit (mobile/strong in particular), then Crossfit might be a great outlet for you to pursue.
Smart boxes will know how to adjust programming to suit your current level of ability, but few in my experience (if you own a box, I don't necessarily mean you) have great knowledge in this capacity still (it's hard to obtain in a weekend, even a few months worth of training would still make it difficult though). If I had to guess I would say less than 20% of Crossfit Boxes have adequate coaching, mostly due to the fact that their owners simply haven't had enough experience yet.
If you add really bad programming and stupid WOD's (just because you can program something, doesn't mean you should -- I'm personally appalled by some of the dumb WOD's I've seen over the years, even some of the official ones; though I've also seen a few finisher gems in there too) and you often have a recipe for disaster.
The thing is that most people don't have the appropriate structure for things like olympic lifting (there are other examples for the gymnastics component as well) and that's why it's not as popular as other sports, it's very hard and you have to have the right body type to be truly good at it. Applying it to people who don't have that body type in excessive volume or intensity often leads to bad things, nearly 1/3 of the population has a shoulder structure that doesn't like much overhead pressing, throw in the desk postures found in North America today and you have probably closer to 2/3's of the population that shouldn't be throwing olympic barbells overhead with any kind of frequency (this is not to say that olympic lifting is bad either, it isn't, it just needs to be applied correctly to the appropriate context). However, if you can't get your arms above your head in perfect alignment, why are coaches loading that movement in the first place?
If you can't get into the right positions first, laying strength over a faulty movement pattern is what often occurs, followed by injury eventually. The younger you are, and depending on your bodily structure, the more resistant you generally are to that, but it's only a matter of time. I spend a lot of my time as a coach, undoing bad movement, which takes a lot longer than just doing it right the first time.
The limiting factor with Crossfit is almost always in the coaching and what I generally view as generally bad high repetition programming (with exceptions of course). Most of Crossfit is skewed towards the WOD and most WOD's are energy system training at high volume and high intensity (meaning Crossfit is really skewed to conditioning as a base, when it should focus on good movement and strength), which can be applied together at the same time but should only be applied together infrequently and in calculated doses.
Personally if I owned a box I would do WOD's (in the context they generally appear) once a week at most, maybe once or twice a month even to benchmark the 'training' (more on that in a sec). The thing that isn't yet obvious to most in the community is that a WOD is the equivalent of a game in any other sport, you wouldn't (just) play soccer games 4-5 times a week and not expect your athletes to get injured. Or in the example of swimming and drowning above, you wouldn't slap a kid into swim meets right away, would you? Without first teaching them how to swim?
This is essentially what most crossfit boxes do, sign up for an onramp and from day one you do a WOD.
That's why we have this thing called 'practice' and 'training.' This same problem is rampant in youth athletics where kids spend way too much time competing and not nearly enough practicing and developing good skills that will aid them in future competitions.
Up until Crossfit decided to turn 'training' into a sport, you used to (and really you still should) go to the gym to 'train,' in order to get better at something (often a sport or something unrelated to being in a gym). Training means practicing, working on your weak skills, acquiring new ones that make you better at your sport and in the context of Crossfit I personally think they would be better served by placing a higher emphasis on the often short 'Skill Work' they place before WOD's (on occasion). If they merely switched the amount of time they work on skill development for the amount of time they spend on WOD's even, most people would be better off. For most of my athletes, I like to see them practicing/training at least 3-5x more than they compete.
i.e. for every competition they have they are in the gym or in a technical practice at least 3 times for every competition on average.
In the off-season I like to see more of that, which is another thing from conventional training that hasn't quite filtered its way into the Crossfit community (or the endurance sport community for that matter). You need an off-season, especially training at that intensity and at that volume of workload.
Anyways, I got off on a bit of a tangent there on ways I think it could be made to be safer overall.
I believe Crossfit has made a very positive change within the world of fitness. What I thought would be a fad 5 or more years ago, has the potential to be so much more than even it currently is. It doesn't look like the organization will be pushing for more regulation or more stringent licensing patterns though any time soon as that's how it makes money really (that and certifications). Based on that I think it will be up to the community to make the ideal changes. That, or somebody smart will come along and offer a similar but slightly smarter approach that builds upon what the Crossfit community has already done with better coaching, and more regulation and moves away from the elitism that is starting to shroud the brand a little bit.
It can be safe in the right box, with the right coach, and I'm secretly hoping for the day I can say that about the majority of their boxes.