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Because temperature and pressure are directly proportional.
The lower you go in altitude, the less pressure there is in the Earth's atmosphere. As a result, as the gas in the atmosphere rises, it experiences less pressure, causing it to expand. When a gas expands, it produces energy. And if it's working, it's wasting energy; and if it's wasting energy, its temperature must fall, because temperature is defined as the average energy of the particles. As a result, if the particles' energy is lower, the temperature must be lower. That's why the temperature appears to drop with altitude.
The reason it's actually colder is because, as you go up in the atmosphere, the Earth's atmosphere feels less pressure the higher up you go. So as the gas in the atmosphere rises it feels less pressure, which makes it expand.