Why are leaves green if chlorophyll is bad at absorbing green light?

Precisely because it's bad at it. Chlorophyll, the pigment that lets plants absorb energy from light, absorbs most strongly in the blue and red parts of the spectrum but is a poor absorber of green. That green light is reflected by structures like cell walls instead of being absorbed, and it's what reaches your eyes. Every green leaf around you is, in a sense, showing you the light chlorophyll uses least.

Chlorophyll was first isolated and named in 1817 by the chemists Joseph Bienaimé Caventou and Pierre Joseph Pelletier, but it took most of a century to work out what was actually inside it: the magnesium in it wasn't detected until 1906, the first time that element had ever been detected in living tissue. Untangling its full structure took even longer, stretching from Richard Willstätter's work in the early 1900s to Hans Fischer's description of chlorophyll a in 1940, Robert Burns Woodward's total laboratory synthesis of the molecule in 1960, and a final stereochemical detail nailed down by Ian Fleming in 1967. As recently as 2010, scientists announced an entirely different form, chlorophyll f, in cyanobacteria.

Inside a plant's chloroplasts, chlorophyll molecules do three jobs in sequence: most of them simply absorb incoming light, then pass that energy along to a special chlorophyll pair at a 'reaction center,' which performs charge separation, releasing free electrons and protons. The electrons that replace them are stripped, ultimately, from water molecules, which is how photosynthesis releases oxygen gas, the source of practically all the oxygen in Earth's atmosphere. The flow of electrons also pumps protons across a membrane inside the chloroplast, building up a force used mainly to make ATP or NADPH, which helps turn carbon dioxide into sugar.