Why is the one-sided overhand bend also called the European death knot (EDK)? Is it safe for climbing and mountaineering purposes?
For certain purposes, the offset overhand bend is not just safe but safer than any known alternative. The alternative name "European death knot" is a joke referring to the fact that to the uninitiated, the knot looks like it wouldn't be secure. It's like the phrase "politically incorrect," which nobody today uses without irony.
There is a common misconception that a knot will slip under a certain amount of load, and that this load is different for some knots than others. Not true. There is a class of knots that physically cannot slip, because the more load you apply, the tighter the knot gets (provided that the coefficient of friction is above some critical value, which in practice will be true, unless you're dealing with a knot that's icy or something). The EDK belongs to this class, as do some alternatives such as the fisherman's bend. These knots do not have slipping as a mode of failure.
The possible modes of failure for these knots are (1) capsizing, and (2) breaking the rope.
Capsizing is a mode of failure in which the knot turns inside out. This has been observed in laboratory tests with the offset figure 8, and is suspected to have been the cause of several deaths in which people used an offset figure 8 as a bend to join two ropes, and then rappelled off of the joined rope. When the knot capsizes, the tails get shorter. If it happens repeatedly, the tails can get used up, and the knot pops open. The EDK is not subject to this mode of failure. Laboratory tests have never succeeded in getting any EDK to capsize, even when it was intentionally dressed very loosely.
Breaking the rope is theoretical mode of failure. In reality, you simply cannot break a modern climbing rope (if it hasn't been damaged) with any amount of load that can be achieved in any realistic climbing situation. I know someone who tried to use a climbing rope to tow a car out of a ditch, and the rope simply kept stretching until the tow truck's tires started to spin. Before a modern climbing rope will break, it will stretch like taffy to such an extreme that it's thinner than a pencil. You simply can't do this in any realistic climbing scenario. It is true that if you stretch a rope so much that it breaks, it will tend to break at a knot. There are classic experiments demonstrating this with cooked spaghetti filmed using high-speed video. The strain required for breaking is theoretically lower for some knots than others, because the radius of curvature of the rope is less. In climbing, this is a total non-issue.
The EDK is safer than other choices when you want to join to ropes for rappelling. The reason is that the knot is less bulky than the alternatives, and therefore less likely to get stuck when you try to pull it down. The situation where you try to pull down your rope and it gets stuck is potentially a life-threatening one, so this is a huge safety reason for preferring the EDK.
A secondary advantage of the EDK is that if you want to untie it after it's been loaded, you can. This is usually not possible with a double fisherman's knot. That's why, for example, I tie my cordelettes and Prusiks with an EDK. Then if I have some other application where I want to use that piece of cord extended rather than looped, I can.
When you tie an EDK, it doesn't hurt to dress it carefully, pretension every strand against every opposing strand, and make sure it has long tails. These steps will even make a potentially unsafe knot such as an offset figure 8 bend hold. However, lab tests have not managed to make the EDK fail even if the knot was intentionally tied in a sloppy way, so even if you forget to do these extra safety steps, you are not actually endangering yourself.
The European Death Knot is commonly used for joining two ropes for an abseil. I would not say it is "not considered safe" - e.g. the British Mountaineering Council's website lists it as a possible abseil knot. Although not the most secure knot it has the advantage that it is small and less likely to snag on edges than larger knots or stronger symmetrical knots such as the double fisherman's knot.
If poorly tied, and/or tied with short "tails" (free ends) then it can invert and come undone under load, which has caused accidents some examples on here. This may be the reason for the name, or it may be due to confusion between this and the similar one-sided figure of eight bend, which is dangerous and can easily invert under body weight.
According to this source its name arose initially in the US where unfamiliarity bred distrust, and because the occasional disaster, likely with the Flat Figure 8 version, caused both knots to be branded with the EDK (European Death Knot) name.
Another source says its name is because this knot looked sketchy for Americans when they European climbers using it.