What are the arguments and proofs that point to Ariel Sharon being a war criminal ?

I do not know from where to start, plenty. To name a few:
1- On the evening of 14 October 1953, a commando unit of the Israel Defence Force (IDF) called Unit 101, under the command of a 25-year-old Ariel Sharon, raided the village of Qibya, in the then Jordanian-controlled West Bank. Their attack involved mortars, grenades and shooting; the majority of the victims were civilians. Sixty-nine Palestinians were murdered that night, two-thirds of whom were women and children. Fifty homes were demolished by the Israeli commandos. Sharon later wrote in his diary that he had received orders to inflict heavy damage on the Arab forces in the village:

"The orders were utterly clear: Qibya was to be an example for everyone."

As the UN observers on the ground documented:

"Witnesses [in Qibya] were uniform in describing their experience as a night of horror, during which Israel soldiers moved about in their village blowing up buildings, firing into doorways and windows with automatic weapons and throwing hand grenades."

The late premier's defenders have tried to argue that Sharon was unaware of the civilians inside these homes. This is nonsense. Again, according to the UN observers,

"bullet-riddled bodies near the doorways and multiple bullet hits on the doors of the demolished houses indicated that the inhabitants had been forced to remain inside until their homes were blown up over them".

2- In 1995, the Los Angeles Times reported that retired Israeli brigadier, Arye Biro, had confessed that he and his paratroops had killed 49 unarmed Egyptian prisoners of war, in cold blood, during the 1956 Sinai campaign. The paratroops' brigade commander? General Ariel Sharon.

"There were exactly 49,"

Biro said, according to the LA Times.

"We tied their hands and made them go down to the quarry. They were startled, broken and shattered... As for the question who exactly shot or didn't shoot the workers at the quarry, why is it important? Between us, the main thing is that they shot."

The US paper said Israeli journalists had

"tried to publish accounts of the killings for decades but [were] prohibited by government censors".

Sharon never offered - and was never asked to offer - an explanation or defence for these killings before he died.
3- Sabra and Shatila. These are the words that should lead off any serious obituary of the former Israeli PM and general. On 18 September 1982, hundreds, if not thousands of Palestinians, in the Lebanese refugee camps of Sabra and Shatila were slaughtered by the Phalangists, a Lebanese Christian militia who had been ushered into the camps with Sharon's consent, blessing and approval. (Sharon, then the Israeli defence minister, had earlier engineered an invasion of southern Lebanon to try and topple the Lebanese government and install a pro-Israeli Maronite Christian regime.)
In 1983, a formal Israeli commission of inquiry, chaired by president of the supreme Court, Yitzhak Kahan, found Sharon bore "personal responsibility" for the Sabra and Shatila killings; "for ignoring the danger of bloodshed and revenge" and "not taking appropriate measures to prevent bloodshed". "It is impossible to justify the Minister of Defense's disregard of the danger of a massacre," declared the Kahan commission.
And it was, undeniably, a massacre. As Al Ahram reported in 2001,

“the count of victims varies between Israel's estimate of 700 to that of independent sources, who say the death toll was as high as 3,500. The exact figure, however, will never be determined."

Or remembered, it seems. Shamefully, on Sunday morning, the BBC's lead news package on the former Israeli prime minister's death didn't deign to mention Sabra or Shatila or the damning verdict of the Kahane commission.
4- According to the Israeli human rights group B'Tselem, at least 240 Palestinians were murdered by the IDF between March and May 2002, as part of 'Operation Defensive Shield' - Sharon's massive military invasion of the West Bank and aerial bombardment of Palestinian towns and cities.
This death toll includes the 22 civilians who, according to Human Rights Watch (HRW), lost their lives in the much-disputed 'Battle of Jenin':

"Among the civilian deaths were those of Kamal Zgheir, a fifty-seven-year-old wheelchair-bound man who was shot and run over by a tank on a major road outside the camp on April 10, even though he had a white flag attached to his wheelchair; fifty-eight year old Mariam Wishahi, killed by a missile in her home on April 6 just hours after her unarmed son was shot in the street; Jamal Fayid, a thirty-seven-year old paralyzed man who was crushed in the rubble of his home on April 7 despite his family's pleas to be allowed to remove him.."

While HRW refused to validate Palestinian claims of a 'massacre' at Jenin, or anywhere else, it did determine that "Israeli forces committed serious violations of international humanitarian law, some amounting prima facie to war crimes". Amnesty International accused Sharon's IDF of behaving as if "the main aim was to punish all Palestinians".
Or as the Israeli sociologist Baruch Kimmerling famously described Sharon's 2002 strategy:

"politicide... [a] gradual but systematic attempt to cause [Palestine's] annihilation as an independent political and social entity".

5- Sharon has been lauded by the obituarists for his unilateral withdrawal of Israeli forces from Gaza in 2005, and the dismantlement of the illegal settlements in the strip. Yet, during his five-year premiership between 2001 and 2006, as Human Rights Watch notes, "the number of Israeli settlers in the West Bank, including East Jerusalem, and the Golan Heights, increased from roughly 388,000 to 461,000" - that is, 73,000. According to Munayyer, Sharon "presided over the single most significant period of Israeli settlement expansion... since the [Menachem] Begin era".
HRW reminds us that

"the transfer by an occupying power of its civilians into an occupied territory is a grave breach of the Geneva Conventions, and a potential war crime".

Such pesky international conventions never bothered Sharon, who said as a foreign minister in 1998 in referring to the Israeli settlers in the occupied West Bank:

”Everybody has to move, run and grab as many [Palestinian] hilltops as they can to enlarge the [Jewish] settlements because everything we take now will stay ours... Everything we don't grab will go to them.“(While addressing a meeting of militants from the extreme right-wing Tsomet Party ,Agence France Presse, November 15, 1998).

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"It is the duty of Israeli leaders to explain to public opinion, clearly and courageously, a certain number of facts that are forgotten with time. The first of these is that there is no Zionism, colonization or Jewish State without the eviction of the Arabs and the expropriation of their lands." Yoram Bar Porath, Yediot Aahronot, of 14 July 1972.

"It's a shame that Sharon has gone to his grave without facing justice for his role in Sabra and Shatila and other abuses," says HRW's Middle East director Sarah Leah Whitson.
I agree, but it is even bigger shame that sections of the media, allied with leading politicians, and answers by Zionists here on Quora seem bent on glossing over those abuses.
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