Radial arm saws always climb-cut. This means that all that radial energy in the cutting edge wants to drag the piece into the fence; it basically feeds itself into the work, causing the operator to need to hold it back. Climb-cuts are special because no matter what the material is, the cutting edge will find a way to make it easier: climbing out of the cut and across the work. It is, obviously, the path of least resistance.
Now add a dado stack to that, with its large surface area of cutters and chip-breakers. A dado stack definitely does not want to go through the stock, when it can move only a few millimetres up and go across the stock.
The operator has to control a cutting head that wants to move toward you, and up. But the operator also has to pull the cutting head through the material and keep it in the material. These are three different directions that the operator has to guide a 3500 RPM stacked carbide cutting head through, at least two of them in opposite directions, and one perpendicular to the others. If you know anything about how humans control the forces in their bodies, you'll notice this is a Bad Idea.
This is why many woodworkers will tell you that cutting dadoes with a radial arm saw is a bad idea. The forces acting on the piece, and the requirements put upon the operator to do this safely, make for a very interesting situation. It is primarily interesting because the vectors of movement change in unpredictable ways much faster than any human can react.
There are ways to make this a less interesting situation. Make shallow cuts. Watch your feed rate. Cut thinner dadoes, or cut them in multiple passes. Engage any new-fangled safety attachments (which are all there to try and mitigate the failure modes just discussed) properly.
And assume it is going to climb up out of knot or some weird grain one day and there ain't nothing you can do about that. Any whirling blade will want to drag a hand into it, of course. The difference here is how that whirling blade wants to do it, and how you might be pushing slightly against that force when it suddenly changes direction.
The main purpose of any power tool is to separate the meat from the unwary operator. Why people specifically warn against radial arm saws and dado stacks is because there are slightly more ways for the tool to do this thing it wants to do.
We won't discuss rip-cutting lengths using a radial arm saw. There are so many better ways of doing this, and so many excellent examples showing why this is a bad idea. If you think table saw kick-back is exciting, just watch how much force can be applied to a piece of wood on a radial arm table when that radial energy is converted into linear motion.
I don't know why anyone would warn against cross-cutting. About the only thing radial arm saws excel at are being portable enough to cross-cut all day to make rafters or whatever. (Though I guess those folks would use "chop saws" which deliberately control for the problems with climb-cutting.)
In short, if you are experienced and follow the rules, accidents using power tools is a "low probability, high consequence" situation. For radial arm saws and dado stacks, people smarter than me consider it a higher probability situation with the same consequence.
