On what basis did Mao denounce Confucianism?

Mao's attacks on Confucianism started with a "Criticize Lin, criticize Confucius campaign.

It started with an attack on the "hegemons," or what we westerners would call the "patriarchy," of which Confucius was the prime (Chinese) example. It continued with attacks on Communist leaders, Lin Biao, and later Zhou En Lai, who were rivals to Mao in the hierarchy. Mao, on the other hand, was a continuing "revolutionary," aided and abetted by his wife Jiang Qing and other members of the so-called "Gang of Four"These kinds of struggles sometimes happen in Communist movements, when some party members want to become the "Establishment," while others opt for continuing revolution.

It's possible that Mao's views also reflect his early struggles with his father. Of the three influences cited in the question, Jiang Jie Shi (Chiang Kai Shek) appears to be the least likely.

Confucianism

On why Master Kong's grave and temples were targeted: Confucianism began as a state-sponsored religion/system of belief during the Han dynasty (202 bce - 220 ce). In its original form, one of the requirements to be accepted as a Confucian scholar was to qualify via taking imperial examination of the Five Classics (of early China).

The other requirement was to participate in rituals honouring Master Kong, namely, visiting his grave and temples. From Religions of China in Practice (1996), p.6:

"Confucianism" is a complex ritual apparatus, an empire-wide network of shrines patronized by government authorities. It depends upon the ability of the government to maintain religious institutions throughout the empire and upon the willingness of state officials to engage regularly in worship."

Activities of Red Guards Against Intellectuals

There are several layers, mainly political, to this question. The missing context are:

1. Mao instigated the Cultural Revolution in 1966. In general, the purpose of this movement was to maintain control and preserve his form of communism. Mao's Red Guards were a direct result.
2. One of Mao's key adviser which led to the Cultural Revolution was Zhou Yang, a literary theorist. His 1963 report, "The Fighting Task Confronting Workers in Philosophy and the Social Sciences" (pdf), was presented to Mao. In this report, Zhou Yang warned against the potential harm of China's intellectuals:

What the opportunists and revisionists dread and hate most and have therefore tried in every way to revise is the Marxist theory of class struggle, and particularly that of proletarian revolution and the dictatorship of the proletariat.

3. It should also be noted that the Communist Party, from its earliest days, have always sought to control and regulate the activities of China's intellectuals. The Yan'am Forum of Literature and Art, led by Mao in 1942, is evidence of this. Merle Goldman's "Literary Dissent in Communist China" (1967) is important and has more on this point.

So, OP's weblink of the 200 Red Guards from Beijing (Jinggang Shan Red Guard Corps of Beijing Normal University) and Qufu (Shandong) desecrating the grave and temples of Master Kong ("Confucius" in Western literature) on 10th November 1966 -- at the beginning of the Cultural Revolution -- is another incident of erasing the memory of China's intellectuals. There should not be anything particularly personal in their attack on the grave and temples of Master Kong/Confucius.

The fact that this group of Red Guards (from Beijing and Qufu) formed the 'Revolutionary Rebel Liaison Station to Annihilate the Kong Family Business' is incidental.

Confucianism and Marxism are in inherent conflict

Confucianism aims for a strictly hierarchical society in which all places are strictly adhered to:

Duke Jing of Qi asked Confucius about governance. Confucius replied: “Let lords be lords; ministers be ministers; fathers be fathers; and sons be sons.” The duke said: “Excellent! If lords are not lords, ministers are not ministers, fathers are not fathers, and sons are not sons, would I be able to eat even if I had rice?”

Marxism aims for a classless society. Furthermore, it holds that the relationships Confucius describes are inherently exploitive. For instance, in A Revolution Is Not A Tea Party, defending Mao, cited this passage and the word "[tribute]" was interpolated into this passage before "rice" -- the Marxist analysis of this was that it was to hold peasants down and let the duke eat the rice he extorts.

Indeed, the conflict goes much deeper than particular attacks on Confucianism. The New Marriage Law gave the marrying couple the right to marry without parental consent, and required their consent, which would be completely unfilial under Confucianism.

As a consequence, regardless of Mao's personal motives, it would be necessary to attack Confucianism to promote Marxism.