Question

why does burning fossil fuels drive climate change?
lets heat escape to space
releases ancient carbon back into the atmosphere
strengthens sunlight
removes oxygen from the air

Explanation:

Fossil fuels contain carbon that has been sequestered for a long time. When burned, this carbon is released as carbon dioxide ($CO_2$) into the atmosphere. $CO_2$ is a greenhouse gas. Greenhouse gases trap heat in the Earth's atmosphere (opposite of letting heat escape), and they do not strengthen sunlight. While burning fossil fuels does consume oxygen, the key issue related to climate change is the release of carbon (as $CO_2$) which enhances the greenhouse effect.

Answer:

Releases ancient carbon back into the atmosphere.