Why do comets grow long tails as they approach the Sun?

Answer: Sunlight and the solar wind push its gas and dust away

Sunlight and the solar wind push its gas and dust away ✓ — As a comet nears the Sun, heat turns its ice into gas that carries dust away. Sunlight and the solar wind then push that material outward, so the tail always points away from the Sun, even ahead of the comet as it heads back out.

The Sun's gravity pulls material out of it — Gravity pulls material toward the Sun, not outward into a tail. The tail forms because sunlight and the solar wind push the comet's gas and dust away from the Sun.

Its speed leaves a trail behind it, like exhaust from a car — A comet's bright tail doesn't trail behind it like exhaust; it points away from the Sun, even when that means ahead of the comet. Comets do shed a fainter debris trail along their path, which later causes meteor showers, but that isn't the tail you see.