Why can dim ultraviolet light knock electrons out of metal when blinding red light can't?

Because light arrives in packets, and what matters is the size of each packet, not how many you send. Einstein proposed in 1905 that light is made of discrete bundles of energy, later called photons, and that each photon's energy is proportional to the light's frequency. Ultraviolet photons are big enough to tear an electron out of a metal; red photons are too small. Making red light brighter just adds more small photons, and an electron can only take one photon's energy at a time, all of it or none.

That is the photoelectric effect: light shining on a material knocks electrons out of it. Physicists expected the opposite. If light were only a smooth wave, a bright beam should pour in more energy and fling electrons out faster, and even dim light should work if you waited long enough. Instead, experiments showed that each metal has a threshold frequency below which no electrons come out at all, however bright the light or however long it shines. Above the threshold, brighter light ejects more electrons, but each one leaves with the same energy.

The effect was spotted by accident. In 1887 Heinrich Hertz put his spark detector in a dark box to see the sparks better, and they got shorter. A glass panel was blocking ultraviolet light that had been helping electrons jump the gap.

The American physicist Robert Millikan was sure Einstein was wrong, because so much evidence said light was a wave. He spent a decade trying to test the theory, and his 1914 results confirmed Einstein's predictions in every detail. Einstein won the 1921 Nobel Prize for this, not for relativity.