I think a better question is not why is it bad, but why did we assume it wasn't?
Let's start by figuring out what we mean when we say "RF radiation". The wavelength can be gotten by looking at the frequency: f = 2.4 * 10^9 Hz gives l = c/f = (3.0 * 10^8 m/s)/(2.4 * 10^9 1/s) or about 35 cm. A typical molecule, by contrast, is more like 500
picometers, or 0.00000000005 cm. Since electromagnetism is gauge-invariant it's not too hard to assume that this EM wave looks like nothing on the scale of our bodies.
Unfortunately, proteins (the stuff of life) aren't typical molecules. They tend to have a very complicated electric structure and they're much bigger than most molecules, closer to the nanometer range, which, a whole lot of math[1] later, means that even RF radiation of this frequency could affect their activity. The cell membrane, itself a huge (relative to molecular scales) macromolecular structure, is also susceptible to polarization, e.g. action potential. DNA fits this pattern too. And in fact, they all have very intricate charge distributions, which need to very closely match the charge distribution of the substrate. Chemical reactions are after all electromagnetic. So a living organism is sort of like a worst-case scenario for a system being affected by radiation. It's full of large and delicate molecules susceptible to electric disruption.
Trying to calculate the E field given an electromagnetic wave going through a human body is basically impossible. So we never really knew if it was safe, we just hoped.
Now, hold on. An AM radio tower can put out as many as a million watts of RF radiation. Why aren't people who work in these towers affected[2]? Well, the wavelength of AM radio is more like 300 meters. That's a whole lot longer, possibly too long to affect anything in our body. In fact: the wavelength of AM is so long that whole tower is an antenna. But more importantly, radiation follows an inverse-square law, and our bodies don't tend to be so close to AM transmitters.
Neither of those are true in the golden age of WiFi, when my ~3 watts laptop RF transmitter sits right now half a meter from my genitalia. Only the aluminium unibody and induced hipster field of my Macbook Pro can protect me.
I can't help but think given the wide spread use of it everywhere for a while that if it had a serious significant effect we would well and truly know it already.
Quite the contrary: if it happens to everyone equally, we might accidentally think it's the result of something else. If it happens to a specific group "users of product X", it's much easier to notice.
[1]: I didn't actually do the math. It's very hard.
[2]: Well, we think they're not affected. [e minor]