You are suffering from a strong mathematical fallacy, based on notation. Rate is the portion of the inititial population that expired from famine. When you use the phrase 'biggest famine' you are talking about raw death counts, not the death rate. If the only two people on a deserted island starved, by your metric, it would be the greatest famine of all time at a 1000:1000 rate. Instead, it's important to note that the 'size' of a famine refers to the total number dead (ignoring initial population), and not the percentage affected of the initial population. Although other regions may have had higher rates (even through antiquity), the initial population of 1950's China during said famines was high enough to negate the lower decay rate.

Conclusionary: Assume two countries/populations, 'Cat' and 'Dog', both have famines. Cat has a death rate of 10:1000, while Dog has a death rate of 50:1000, five times larger. Clearly, Dog has had a far more devastating famine, as a greater portion has died. However, lets assume that Cat initially had a much larger population of 20 million, while Dog has a pop. of two million (1/10). Cat will have suffered 200k deaths, while Dog suffered 100k deaths. Cat had a famine twice as great (numerically), despite having one-fifth the death rate.

Another issue here is that you list a rate for each year; they stack! The death rate for 1959 only applies to the people who didn't die in 1958! So lets assume a model population of 1000. The first year, 1958, 11.98 die leaving a pop of 988. The next year, 1959, 1.459% of the remaining population dies, leaving 988 * (100%-1.459%), or 973. Repeating this (iterative) process through your last point, 1961, gives a remaining pop of 935 after the four year period. That means that in the 4 year period, the famine caused a total loss rate of 65:1000!

So, someone already seems to have answered why using raw death rates without context is pretty bad. As such, I think it falls to me as to why this is considered to be abnormal. After all, just numbers isn't going to tell the full story; as such, I'll do my best to give a condensed version of what happened behind the numbers that leads people to call it a famine.

The reason why the years during Great Leap Forward is considered to be a famine is because the events set off by said Great Leap led to a large number of deaths from starvation and overwork.

The Great Chinese Famine is linked to the Great Leap Forward for many reasons. There is no singular cause as to why it happened, as it was part of multiple events, including (in no particular order):

1. the Three Red Banners, consisting of
   • the General Line, which encouraged "greater, faster, better, and more economical" and rash spending in an attempt to industrialize quickly and beat the US and the UK with regards to steel production within 15 years,
   • the Great Leap Forward, which was essentially the General Line in action, and
   • the people's communes, which was intended to abolish families as the primary production unit, dismantle private property, and otherwise allow the state to have more control over the economy and people's lives
2. rather violent (and often deadly) anti-rightest campaigns that discouraged people from speaking the truth lest they be the direct victims of "struggle",
3. the development of commune kitchens,
4. the Exaggeration Wind, which led people to overestimate production totals and production quotas to an absurd degree,
5. the over-extension of manpower towards building projects that were often badly mismanaged and/or abandoned,
6. the over-confidence of cadres, who in at least one case ignored geography and planted crops that were not suitable for that particular area to that province's peril, and
7. a totalitarian system that kept the higher ups from recognizing their own wrong doings and which magnified problems down to the grassroots level.

Honestly, there's probably more reasons than that, but I'm doing my best to focus on the bigger ideas, because it's just a jumbled mess of events.

The Great Leap Forward, as the manifestation of the General Line in action, wanted to industrialize as quickly as possible, with the intention of becoming a great communistic country that can surpass the production power of Western powers within 15 years. Mao envisioned that with enough dedication and enthusiasm (and with the right kind of thinking), the country could join communistic paradise within a few years. There were some leaders within the party who opposed what they saw as "rash advance", as the country was putting large sums of money into industry with very little benefit, and tried to slow it down in early 1958, prior to the introduction of the Great Leap Forward. However, Mao was not happy about this and reverted it, and those who had opposed it later gave self-criticism and otherwise followed Mao's line, praising Mao's genius and otherwise agreeing with whatever he said. Speaking up and saying "this is a bad idea" was political suicide. Disagreeing with Mao was seen as a counterrevolutionary act; with that, people who spoke out against Mao's ideas were seen as "white flags" and capitalistic elements that needed to be rooted out and replaced with "red flags". When something went wrong, it was the fault of counterrevolutionaries who were trying to sabotage the Great Leap and socialism in an attempt to go back to bourgeoisie ways. People who did not agree with Mao completely could be and were often violently struggled against, and in many cases it turned deadly. Under this type of environment, people who spoke up and told the truth were labeled right deviationists and punished. There was no incentive to tell the truth, so there was more incentive to lie. Lying became the means of self-preservation and survival.

In addition, the different provinces were in competition with one another. Because of the emphasis on "greater and faster", provinces did not want to be the ones left in the dust. And with people overexaggerating their accomplishments to absurd amounts (like claiming that they were able to plant 1765 kilos per mu in a satellite testing field in Hunan), people were encouraged to exaggerate and make up higher and higher figures, which led to higher production targets, which led to even higher figures regarding crop yields.

Unfortunately for the peasants, these higher figures were used to calculate how much the state would procure as their share of the crop. In many cases, the procurement quota was set so high that even after every single grain was taken away (leaving nothing for the peasants to eat), it wasn't enough to satisfy the quota. New campaigns started up, to fight against "false reporting and private withholding". People were being beaten and tortured in the belief that they were hiding grain away from the state. When this turned up nothing, cadres from every level lied about how much they were able to procure from class enemies, which in turn just exasperated the problem and made it oh so much more violent than it was.

The people's communes made it so much worse. These communes were rather large, with the average commune consisting of over five thousand households. They were also really inefficient, since many communes were spread out over vast tracts of land. People were required to sign up for a commune, lest they were labelled as white flags and targed for struggle. Once in the commune, their property was seized without compensation, and manpower was sent out en masse to work on large industrial projects (to the point that there were not workers available to plant or harvest crops). Fields were left fallow, peasants were ordered to work on other projects (and depleting manpower from agricultural pursuits), comrades were highly unrealistic with their demands and ignored geography, and it was really inefficient (to the point that over 100 peasants were sent to work one mu of land in one case). In addition, the people in the commune had to eat in the communal kitchen, which had its own set of problems.

The communal kitchens were part of Mao's dream of free food for everyone, something that was important in his dream of Communist Paradise. In Mao's mind, this would free up more people to work on building a communistic society, as there would be less people having to spend time focusing on cooking food. They offered a large variety of food for free, and everyone in the commune was able to get food from there so long as they did their work. The problem is, these communal kitchens were highly inefficient and led to large amounts of waste. The inefficiency comes from multiple factors:

1. Previously, each household would cook as much food as they would need in their own homes. The people's commune would just cook vast amounts of food for people to eat, ignoring individual needs.
2. Cooking small amounts of food didn't require that much fuel for heat. Cooking large amounts of food to feed an entire commune required people to cut down trees and burn the lumber to get enough heat to cook.
3. People were encourage to eat as much as they wanted. So they tended to overeat. Food that was saved for entertaining special guests and holidays became standard daily fare, and the central leadership would constantly talk about "what to do with the extra food", leading people to believe that there was vast stores of food stored somewhere. In Jiangxi's Xiaogang Commune, there were no restrictions on how much rice one could eat, and some members would gorge themselves, bring excess amounts of food home, and feed leftovers to livestock -- leading to villagers in that commune to devour "seven or eight months' provisions in five months" (Yang, p. 189). Oops.
4. Communal kitchens required large amount of manpower needed to prepare the food. This reduced work points, because so many people were dedicated to taking care of the kitchens, further depleting agricultural pursuits of workers.

In addition, commune members were required to eat at the kitchens (or at least collect their rations from the kitchens), which may be a rather long distance from home. Some people had to travel 15 kilometers to reach the kitchen, spending a good part of the day just traveling to get food. If you didn't work your share (or pissed off a cadre), you could be denied food, leading people to starve. Quality of the food was abysmal, leading to inedible vegetables and dung in the congee, and inevitably people began to get sick. Rations were controlled by the kitchen; even though households technically owned these rations, the kitchen had the actual grain, so people had to go eat at the kitchens. As such, when communal kitchens ran out of food and had to shut down, people were left starving.

When the famine began to take place, cadres did their best to cover it up. Peasants were barred from going places (to keep them from running away or telling people about what was happening), letters were seized to keep word from going out, deaths were under-reported using various means, people were forbidden from telling the truth under political pressure, etc. Word would not reach the Central Committee until millions of people had already perished. Even when people were sent out to figure out how bad the famine was, officials were terrified of telling the truth, lest they earn Mao's ire and be punished for telling the truth. Eventually, something was done, and the Great Leap Forward was abandoned, but by then, millions of people were dead from starvation.

---

I should note that this is a very brief summary of the story behind the numbers. The issues behind it are more complicated than this, and while I did my best to summarize and give highlights, this is woefully incomplete and will inevitably gloss over other related problems.

Source: Yang Jisheng's Tombstone

This statistical debate around the Great Leap Forward is fascinating, but I think /u/ghosttwo's point is really important: considering the GLF in that way can be useful — but it doesn't tell anything like the whole story. It's a good way of observing trends within individual countries, but elides crucial context and gives a warped sense of scale when making broader comparisons.

Alfred L. Chan (whose book Mao's Crusade: Politics and Policy Implementation in China's Great Leap Forward is really excellent) gives a bracketed estimate of deaths during the GLF of 15 to 45 million, of which most "were unintended casualties of famine. The others — three or four million of them — were the human detritus, of [Mao's] epic struggle to transform China."

There are two reasons, I think, why the Great Leap stands out as one of the largest and most notorious famines in history: first, there really are simply few other documented famines which claimed as many lives (though, as we've already established, there were famines that killed larger proportions of a given population). What's more, you're talking about a period of less than three years.

Second, and more interesting/troubling, is the human factor: this famine wasn't just the result of drought or failed harvests (though they were major contributing factors.) It was exacerbated by a truly extraordinary attempt at economic and social engineering that left rural China incredibly vulnerable. It was, in part at least, a man-made catastrophe.