This question bothers many of those, who just got involved into the topic. And it makes sense. I mean, there a number of airborne units in Afghanistan, why would they be there if they were not practicing parachuting behind the enemy lines?
The myth becomes obvious and stupid to anyone who is even a little bit familiar with the geography of Afghanistan or the course of the Soviet-Afghan war. Let's discuss it in details.
Where did the myth came from?
The nature of the myth is unclear, but we have some pretty good theories. The first one comes from early 80s, from the Soviet Union. By 1982-1983 the war in Afghanistan was discussed by the citizens. It was still a taboo topic on public, but in private, those who were involved somehow, would talk about it. And this is when the first myth has been developed. It stated, that during the initial stage of the invasion, the 103rd Airborne Regiment was airdropped at the south border of Afghanistan. The myth claims, that the absolute majority of personnel, up to 70% were killed during the operation.
Of course, now we know, that this myth is not based on anything. A completely made up story. However, there was a plan to perform an airdrop at the Kabul airport at the beginning of the invasion. The plan was scrapped due to associated risks and bad weather conditions. The 103rd Division was delivered to Kabul on airplanes, and they unloaded in regular method - by dismounting a landed plane. One of the IL-76 planes carrying the paratroopers has crashed, during the invasion period. This was one of the biggest one-time personnel losses experienced by the 103rd Airborne Division.
Terms confusion
Another possible explanation is the confusion in terms. In Russian language the word "desantirovanie" means "landing". And it is usually assumed by many, that it means "air-landing". So the simple construct of airborne units and landing in the same sentence feels like it is all about parashooting. But in reality, "landing" can mean any sort of landing - from a ship, from a helicopter or from a ground vehicle.
The airborne units, just like infantry units, would participate in mounted operations rather often. And they would, in turn, do landing from the APCs and from helicopters. But even helicopter landings would mean that the helicopter would either touch the ground or would be 3-5 meters above it, so that soldiers could jump put of it without the parachutes.
Problems with airborne parachuting operation in Afghanistan
Thinking about the theoretical problems with the airborne operations during the Soviet-Afghan war, couple of point would come in mind.
It was impossible to jump behind the enemy lines. Simply because there was no front line, and so there were no enemy lines par se. Any sort of en-masse airborne operation would make little to no sense
The geography of Afghanistan. It is not a secret, that Afghanistan is quite rocky and has lots of mountains. To perform a safe operation, paratroopers have to be dropped on a flat land. The Registan Desert would be quite a good place. But, for obvious reasons, mujaheddins could not hide there in any meaningful numbers. And even if they could, it would be much simpler to roll there on the wheeled armored vehicles.
The parachutes were likely to be lost. Soviet Army was not a fan of loosing material supplies, and organizing parachute collecting teams would be somewhat complicated.
A lot of equipment would have to be dropped separately. Soviet Paratroopers were trained to be dropped behind the enemy lines, with limited supplies and with little chances for resupply. Somehow this was considered a plausible idea for the Cold War go hot scenario. However, after invading Afghanistan, everyone quickly realized how much supplies every soldier and every unit needs. Paratroopers would often carry around 50kg of equipment on them, during the dismounted operations. These supplies would have to be dropped separately, risking loosing them. Otherwise they could be delivered by the helicopters, but then the question would stand - why not deliver soldiers on helicopters as well?
Landmines had to be taken into account. While a trained soldier can spot a mine when walking, he has little chance to avoid it when landing on a parachute.
Sand bags instead of paratroopers
There is another funny story, which belongs to this article. At the end of 1987, during the operation "Magistral", the fake airborne operation was performed. Instead of paratroopers, the sandbags were dropped on parachute, imitating the real airborne operation. Mujaheddins opened fire, while the "paratroopers" were in the air. This gave out most of their firing positions, which were later destroyed by the Air Force and artillery strikes.
Personally to me, this story sounds more like an army joke, rather than a real deal. First of all, I have heard this story in many variations - in peacetime during the training, in Chechnya and so on. Secondly, I was unable to find any people who have seen this operation with their own eyes. And lastly, the story was first told and pushed on TV by the last commander of the 40th Army - General Gromov. And we all know how little trust Soviet/Russians officials have.
Actual jumps
But of course, actual parachuting jumps were performed in Afghanistan on regular bases. First of all, both Soviet and Afghan pilots had to take regular parachuting practice in case of the emergency airplane exit. and given the number of aircraft losses during the Soviet-Afghan war, this was not done for nothing - aircraft were lost constantly and parachuting practice surely helped to save some lives.
The Afghan Commando unit was also notorious for parachuting training. As they were trained in the Soviet style, they were practicing parachute jumps of regular bases. Khatool Mohammadzai, a famous Afghani female paratrooper, has performed over 600 jumps in the course of her career. She would later become the first Afghani national female General, after the 2001 invasion of Afghanistan.
Material part of the parachutes
There is another interesting story associated with the parachutes in the Soviet airborne regiments. After the invasion, when it became clear, that there will be no combat or practice jumps, the majority of parachuting equipment was sent back to the Soviet Union. Officers and warrant officers, who were in charge of parachuting, were reinstated on new positions, replacing their fallen or injured comrades.
The lack of parachutes caused an unexpected problem - the lack of material for the lanyards, which were essential accessories of the demobilized paratroopers. Back in the Soviet mainland, there were plenty of decommissioned parachutes, which were vandalized by the paratroopers for their white slings. Since there were little parachutes available in Afghanistan, it would lead to soldiers disassembling rocket flares and taking the small parachutes from inside of them. The funny part is that some of these flare were assembled back, but without the parachutes. So when it was actually used during the firefight, the flare would just go up and then fall straight down, without actually staying above the battlefield providing the expected light.