Why energy usage serves as a good general estimate of carbon emissions

• The vast majority of energy comes from fossil fuels.
• Until technology improves, renewables & nuclear are in very limited supply.
• Until technology improves, most road vehicles burn gasoline or diesel.
• Most goods are not manufactured in places with lots of renewables.
• Fossil fuels are responsible for most of the world's greenhouse gas emissions.

Thus,
When it comes to climate change, energy usage is the main issue.

Side note:
When it comes to habitat loss, land usage is the main issue (even though the CO₂ emissions involved are more moderate). Food agriculture is the worst offender here, even though it uses only about 2% of the world's energy.