Larger surface area to volume ratio increases the amount of area in contact with air in the lungs to allow for uptake of oxygen and release of carbon dioxide. Basically with a larger surface area, carbon dioxide in the blood capillaries are easily released and oxygen is easily taken up, increasing efficiency of gaseous exchange.
Plants take in carbon dioxide from the environment for photosynthesis. Because trees are large, they need a lot of energy, which likely results in a lot of carbon dioxide being removed from the air. If they’re chopped down, there will be fewer trees to remove the extra carbon dioxide from the air.