There is no real substance for India-China enmity. In 1962, Nehru was acting like a CIA agent, hosting CIA planes & setting up Tibet government in exile which made China angry.
India News:U.S. planes used Indian airbase to snoop on China
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If it was just about helping, India could have given refuge to Tibetans but Nehru went one step further to set up Tibet govt in exile. To make things worse, Nehru pursued a forward policy seeing Chinese problems with Tibet which finally made China react. Although Nehru was unelected leader installed by UK, it was Indians fault to be completely stupid and accept him as authority. Blaming China is simply being unreasonable and arbitrary. How would India act if China sets up Kashmiri govt in exile? This is also why Vajpayee govt accepted Chinese control of Tibet and ended the annoyance.
As for 2020 clashes, it was not armed clashes but with sticks and stones and unlikely to be commanded by either of the leadership (no one will command their soldiers to fight with sticks). Also, India was trying to settle border dispute by sneakily trying to conquer additional peaks rather than China trying to conquer inch by inch, although this time it was not at the behest of CIA but just to secure the borders as the borders is closer to Indian population centre than Chinese. This is also why neither China nor India publish any info nor made any statement on the actual background of the clashes and it was all just media hype.
The complexity in India-China relationship arises because of strategic interest on Pakistan & middle east, mainly for the oil needs. India does not like anyone helping pakistan but China has no other way of getting its oil interests secured. India is wary of China getting too close to Pakistan & middle east to get major hold of oil supply and replace USA which will act as a continued external interference to Indian affairs with just the external agent switched from USA to China.
India-China has no cultural enmity as both are ancient civilisations and have been commonly harmed by the west. India is currently following a policy of neutrality with China. This is also why India refused to host Uighur separatists or support Hong Kong protests- both were western sponsored & India wanted no part in it. But India does not want China to be the next superpower by replacing USA's dominance in middle east but instead wants a multipolar world. Hence India won't ally with China either. This is why Jaishankar termed relation with China as "complex". It is not rivalry, enmity but simply greater geopolitical game taht transcends bilateral relations.
So, coming to war scenarios, China is no real threat to India. Indian 2 fronts are Pakistan & Bangladesh, not China. BD is small but its people have massive hatred against India and is an easy target for foreign agencies to set up anti-India sentiments. However, India uses China's name as a dummy target to justify defence developments and procurements as one can't really use weaklings like Pakistan or BD to build up major capabilities. But its is just a ploy/hype rather than real threat.