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Some technical analysis is based on human psychology. (Thread).
What you call a "support" is often a point when the stock stopped before. If it was at 1,000 and fell to 850, and zoomed back to 1,200 you can hear people thinking if it ever falls to 850, I'll buy.

That's why 850 is a "support" because enough people say that's the point to buy.
A "Resistance" is similar. A lot of people buy at what they think is a low . Imagine the stock above fell to 850, and then people bought but it still went further down to 750. Now the 850 buyer is thinking "I'll get out when I break even, i.e. at 850"
So when the stock starts to go up, it hits 850 and then there's a wave of selling by this break-even crowd so it "resists" the further upside and might fall back down too.
So for example, this chart:
Many moving averages are also used, and then there's complex other things, from RSI to Supertrend to what not. Those have interesting relationships with subsequent behaviour too - so the seller at resistance then feels FOMO at some point when the stock goes further up etc.
Humans love trends and momentum. We understand this innately. Which is why we are surprised when trends break - not because we don't understand averages, but because trends set unrealistic expectations sometimes. (Except in HDFC Bank Results please, I know)
When people do technical analysis that's super complicated, and it works, then my answer to why it works is "I don't know". Mostly, my feeling is, it's all rooted in our greed (trends, momentum) and our fears (break-even, loss aversion).
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