The first major standoff at Depsang happened under Manmohan Singh. And under Modi, Indo-Sino relations were actually pretty good until last year. Even after Doklam, Modi and Xi held two informal meetings.
The rest has already been discussed. In the areas you are referring to, China had been building infrastructure for decades. For example, in Raki Nallah and jeevan Nallah, China had roads leading to its claim line even before 2010. Even if Indian patrols reached certain areas beyond the LAC between those two lines, That area was always dominated by China due to superior infrastructure(until recently) and geographical hallenges. For example, Indian patrols can only go on foot past the bottleneck, and in Pangong, finger 4 acts as a natural barrier and prevents connectivity with the motorable road from Lukung, while China has a road from Sirjiap(well east of finger 8) to foxhole point, on the eastern side of the finger, which is basically a flat beach. The western part is dominated by the ridge. Col. Dinny, who has led patrols there, has explained all of this, but apparently he is a bhakt.
Anyway, this standoff was not just about the areas between the red and pink lines in the map you posted a while back, although China probably did want to further secure its presence in the area. It was about China trying to shift the lac westward to match its historic claim. Otherwise why was China initially demanding India vacate Dhan Singh Thapa as a condition for disengagement, and why did the Chinese Foreign ministry claim the entire Galwan Valley is part of China? The same situation applies in Demchok/Chumar where China claims the entire sector. China's initial conditions for Pangong Tso were in no way met, the reason why disengagement on Pangong took so long was because India refused China's conditions until they were revised to what was suitable to India.
And it wasn't just India patrolling China-claimed territory. PLA patrolled well into areas claimed by India. For example Gen. Sharma clearly said that just like India would patrol to its pps, PLA would patrol to the Track Junction and Burtse, well sithin Indian claimed territory. Now both sides are blocking each other at the bottleneck.
Quite right about the first standoff happening under Manmohan Singh but Doklam sparked a greater escalation of border confrontation. While Modi and Xi had their meetings, it's evident the informal "agreements" from those meetings never amounted to any positive or constructive de-escalation. You will blame it entirely on China and a Chinese nationalist would blame it entirely on India. That's been discussed.
India patrolled up to and beyond finger 4. It patrolled up to India's own claims (not including Aksai China's eastern borders for obvious reasons) within this 20% stretch. If you want to call the situation of China demanding India vacate DST and claiming Galwan valley HS etc, why ignore that India claims all this as well. You're using China's claim which has always been around since the 1950s, as some sort of reason for the standoff. India claims land as well so asking
"Otherwise why was China initially demanding India vacate Dhan Singh Thapa as a condition for disengagement, and why did the Chinese Foreign ministry claim the entire Galwan Valley is part of China? The same situation applies in Demchok/Chumar where China claims the entire sector." is no different to me claiming that India instigated this stand off to push LAC to blue line in that map in an effort to take at least 20% of this historic legacy dispute, of which China has already won 80% after the 1962 war. If anything this makes much more sense.
Anyway in seriousness, to answer your question which DOESN'T prove your point because come on, have some logic. Why did China demand India vacate DST? Well because it is within the disputed land. Why did China claim Galwan valley? Well because it's a part of the historic dispute. The exact lines of claims matter and they aren't actually clear when it comes to Depsang but clear enough when it comes to Galwan. Same for Demchok where both claim it all.
So your theory that China's been trying to push the LAC westward doesn't hold water at all because it's immediately disproven.
1. China already took control of a great deal. If it's purpose was to push the LAC which it achieved, why would they discuss disengagement terms with India? It took control for about 9 months. India refused to militarily challenge and talked with China. If China's point was to take control, why would they achieve that and then negotiate disengagement terms after winning the objective?
2. You ask why China wants India to step back. Well that's again answered with what happened on Pangong. China wanted India behind F3 which is basically China's claim line realistically speaking. In return for India stepping behind F3 and guaranteeing China that it will not patrol beyond F3, China disengaged PLA. The same with the other areas where China demands India step behind in return for standoff to disengage everywhere along this border. There is no other reason and nothing unclear about this. It's not so that once India vacates DST, China will capture it lol. That's not how diplomacy works and not how China could possibly act after agreements. That would be akin to India vacating F4 and going behind F3 only to have PLA not only keep F4 to F8 but also advance to F3. Did that happen? No.
China very simply wants India to vacate the disputed 20% and make guarantees that it will not patrol it because patrolling it can potentially escalate the situation especially if command breaks down.
This is why China demands India vacate xyz for the standoff to de-escalate. India refuses to because it correctly understands that if they vacate xyz, India totally loses their claim for the 80% they've lost since 1962. Not only that but they also will lose access to the 20% in terms of patrolling but of course India will formally still claim the 100%. China wants the 20% to become a buffer. It has no need to control it so long as the 80% it already controlled for 60 odd years to maintain status quo and well out of Indian invasion reach unless India step into and over the 20% which they'd provide guarantees not to a la Pangong F3 ->