Curse of Dimensionality
The way data becomes uninformative as columns are added, because volume grows exponentially while your row count does not.
The usual gloss is "the data gets sparse", which is true and not the part that hurts. The sharper statement is that distances become nearly equal: as dimensions rise, the ratio between the farthest and nearest neighbour tends toward 1, so neighbours stop being distinguishable from strangers.
Measured on 500 uniform random points, that ratio is about 42 at two dimensions, 5.7 at ten, and 1.4 at a hundred. A nearest-neighbour method then picks the five smallest of five hundred numbers that sit within a third of each other, and noise decides the winners. Everything distance-based inherits the problem.
Two other consequences follow. Covering a space to fixed resolution needs rows growing exponentially in the number of columns. And once columns outnumber rows, an unregularised linear model can fit any labels exactly, including shuffled ones.