How much evidence is there against man-made famine in regards to the Holomodor?

Achtung: This is a highly controversial topic with a multitude of viewpoints. I'll start off by giving a very basic overview of the different currents of thought on the topic, before delving into the one that I find the most productive. There's few easy answers here though.

But let's go on.

Today there are roughly three main schools of thought on the causes of the famine:

The first is that this was a genocide or other attempt at ethnic cleansing. To be blunt: Stalin deliberately engineered a famine to massacre Ukrainians. This the official Ukrainian position and was popularised in the West by Robert Conquest.
(Conquest's current position is that the famine was not deliberately engineered but that Stalin took advantage of the impending crisis to either fail to prevent it and/or withhold aid to the Ukraine.)
The famine was not planned but resulted from gross Soviet economic mismanagement, as part of its frenetic industrialisation drive. Responsibility still lies with the Soviet regime but the deaths were not deliberate and cannot be considered genocide. The most interesting advocates of this view are Davies and Wheatcroft, whom I'll draw on extensively below.
The famine was an accident resulting from entirely, or primarily, natural causes. The state is largely or entirely innocent. This is rare in academia (Tauger is the only one who springs to mind) but still surfaces occasionally in works of apologia.

Of these, I find it hard to credit either the first or third. There is little evidence that Stalin set out to deliberately starve Ukrainians to death. Instead the Politburo 'discussions' show a leadership largely uninformed, out of touch (to the point of delusion) and struggling to keep pace with events. But it was also brutal and callous and engaged in an immensely wasteful campaign of industrial and agricultural reform.

Indeed, even a more cursory examination of the broader Soviet economy in these years reveals the degree to which this was not simply a Ukrainian problem. Serious food shortages were endemic across the entire USSR in these years, as the entire economy tottered. Almost half the population (some 70m citizens) lived in areas marked by famine - that is regions in which mortality was over 20% greater than normal. Even non-famine regions saw extreme hardship: mortality rates rose across the board, rationing was introduced, birth rates fell and there was sharp discontent on factory floors over 'starvation rations'. In some areas, ie Kazakhstan, the famine conditions were even more atrocious than the Ukraine.

So the picture that emerges is of a general agricultural collapse, one not isolated to the Ukraine. This was not something that the leadership wanted: the Stalinist elite was, as always, fixated on fantasy rates of growth. An agricultural collapse (which threatened both exports and urban industry) did not factor into this.

Yet such a collapse was certainly a product of their policies. Davies and Wheatcroft identify four key factors in the famine:

Over-extension of the sowing area: Ever more ambitious targets (and quotas) from the centre led to greater land area being sown - at the expense of eliminating/reducing fallow land and crop rotation. Yields suffered as the soil was exhausted and disease ran rampant.
Lack of draught power: The collapse in livestock numbers following collectivisation had a serious knock-on effect on grain cultivation. The number of horses in service fell from 32m in 1928 to 15m in 1934. The production of tractors came nowhere close to making this gap up.
Quality of cultivation: Together with the rest of the chaos (demoralised peasants, creaking transport, etc) the above factors had a direct impact on the grain yields. The quality of the ploughing, sowing and harvesting was all very poor.
Weather: Finally, the weather was indeed poor over the period 1930-34. It wasn't just draught but the spring sowing seasons in 1931 and 1932 were unusually cold and wet. This was even more damaging than usual given the poor quality of the cultivation.

Of those four factors, at least three are direct products of the disastrous collectivisation drive and continued misguided, ignorant and damaging policies from the centre. But. But such policies were not intended to stifle production, quite the opposite. As in industry, the Stalinist elite expected production to increase, not crash. The quotas imposed can easily be explained by an elite following its own delusional grain plan, while ignoring the reality of encroaching famine. (As it was, it wasn't until early 1933 that the leadership, including Stalin, were convinced that there was a famine.)

So was the famine "man-made"? In the sense that it was the product of soviet agricultural policies then, yes. But was it deliberately engineered? No. I've seen nothing to suggest such. This was a general economic crisis that affected the entire USSR and it's extremely hard to picture a scenario in which Stalin would deliberately bring the economy to the brink of collapse. Instead it makes more sense, in my view, to see the famines as an unintended consequence of disastrously incompetent agricultural policy.

Of course, that in no way absolves the Soviet leadership from responsibility. Millions died because of their misguided policies, even if that was not the intent. Moreover, legitimate questions can be asked about the leadership's failure to note the early warning signs (remaining delusional until it was too late) and the nature of their response. But that's a different discussion to one of genocide.

Sources

I've drawn a lot from it above because as far as I'm concerned Davies and Wheatcroft's The Years of Hunger is the definitive economic work on the famine. It reconstructs, in some detail, the shifts and flaws of Soviet agricultural policies in this period. It's a great piece of scholarship. Also worth noting, in the same series, is The Socialist Offensive.

For the impact of the famine on urban areas, see Rossman's Worker Resistance under Stalin and Davies' The Soviet Economy in Turmoil.

Livestock figures came from Davies et al's Economic Transformation of the Soviet Union. For an introduction to the chaos of collectivisation, Alec Nove's Economic History of the USSR is a good place to start.