Why do trendlines work?

I will also add another comment to follow up regarding trend lines.

Make sure that you plot out your trend lines on multiple timelines 5min, 15min, 1h (if your a short term trader like me)

This will give you a better idea of where the trend is actually POTENTIALLY going.

In my opinion trendlines work because lots of traders pay attention to them, including algos. This basically creates (not every time) a quite persistent market anomaly, basically a self-fulfilling prophecy

Trendline works base on market liquidity.

There are many pending order buys and sells have been put in the market. Those orders are placed base on speculation to fundamental events.
When market moves, either by sentiment or fundamental, the price will struggle heavily in the area where many orders are being placed.
When sentiment is considered stable, market will move in specific range up or down, like a stair. This is the reason on trendline works.

Sometime sentiment / fundamental changes, stability is disturbed. It breaks current trendline and create new trendline.