Because it has aspects of truth. The image from Enemy at the Gates, of proper Red Army soldiers being handed rifles for every other man... that isn't what was happening. A few instances early in the war of this happening are better attributed to poor logistics, than an inherent lack of arms. But what these images most likely are drawing on are the civilian levies, or Narodnoe Opolcheniye. Their use can be seen at least through Stalingrad. To quote regarding one notable incident outside Leningrad, (from Beevor):

Altogether over 135,000 Leningraders, factory workers as well as professors, had volunteered, or been forced to volunteer. They had no training, no medical assistance, no uniforms, no transport and no supply system. More than half lacked rifles, and yet they were still ordered into counter-attacks against panzer divisions. Most fled in terror of the tanks, against which they had no defence at all. This massive loss of life–perhaps some 70,000–was tragically futile, and it is far from certain that their sacrifice even delayed the Germans at all on the line of the River Luga.

As you can see here, there was a decided lack of arms. A similar defense was mounted at Stalingrad, where the workers of the Barrikady Ordnance Factory, the Red October Steel Works and the Dzerzhinsky Tractor Factory executed a desperate delaying action on August 25th. In that case, Stalingrad was practically undefended, and the Soviets needed to do anything they could to slow down the German advance, and gain time to bring more proper troops up. Another famed incident from that point was an all-women's AA unit that was pressed into service for anti-tank duties (and all died doing so).

So anyways, that's the sum of it. There is some truth to the matter, but it is basically taking verified instances which were not too common, and dictated by certain circumstances, and amplifying it into the standard practice that it was not.

It's not so much that they were unarmed as they were under-equipped and poorly coordinated compared with troops from the States and from Western Europe. In the early days, they were very poorly mechanized and their industrial base could not keep up with the demand for replacement munitions and equipment. Particularly telling were shortages of radios, aluminum and rubber products. They were able to get their shortfalls of these from the US.

If you're interested in Lend-Lease and you're data-driven, I recommend Feeding the Bear by van Tuyll.

For a long time we were relying on some very self serving German accounts of what happened in the War in Russia. After all it wasn't our "Eastern Front". Some of the German narratives are curiously inconsistent about who was underarmed and when and most are nothing but unabashed apologetics. There were instances in the First World War of under equipped Russian infantry attacking and no doubt similar things could have occurred in the disastrous summer of 1941.

Didn't the Russians try human wave tactics (with armed troops) against Finland at the start of the winter war and this lead to them realising human waves no longer worked?

To piggy back somewhat on this- how effective was scorched-earth tactic (by the Russians) at the beginning of the war.