Why are some stars red and others blue?

Answer: Surface temperature sets the color

Different chemical compositions — Wrong. Composition changes which dark lines appear in a star's spectrum, but the overall color comes from how hot the surface is, not from what the star is made of.

Surface temperature sets the color ✓ — Correct! A star glows like a hot object, so its color tracks its surface temperature. The hottest stars shine blue-white, like Rigel and Spica, with surfaces above 30,000 K. Medium stars look white or yellow, like the Sun at about 5,800 K and Sirius. The coolest stars glow red, like Betelgeuse and Antares, around 2,000 to 3,500 K. The peak wavelength shifts toward blue as temperature rises, which is why the O-B-A-F-G-K-M sequence runs from hot blue stars to cool red ones.

Age determines star color — Wrong. A star's color can change as it ages, but that happens because its surface temperature changes. At any given moment, color tells you the current temperature, not the age.