Because your body is Oxygen Debt, and lactic acid is being produced in the muscles at a higher rate, so your body pumps blood to these muscles, quicker, to remove the lactic acid and supply them with glucose.
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Your body breathes to take in oxygen and expel carbon dioxide. When you are smoking, you are taking in all kinds of things with the oxygen. Those foreign items are going the same place your oxygen should go - the lungs and then picked up by the blood. You are out of breath because you are depriving your body of oxygen at that time. Your lungs also sustain some damage from those foreign items and you may have trouble breathing until they have healed.
I personally suffer from Asthma. I get very breathless at times. Some people say that people who have asthma are breathless because they are over weight, this is not actually the case. Anyone can have asthma really.
People who have asthma get breathless because, their heart is not used to running fast and can not handle it.
Also just another note, I think it's because with asthma it causes the smaller airways of the lungs constrict (or close up) which will cause a shortness of breath and make it harder to breath.
There are a number of things that may cause running out of breath. In most cases, this is due to overwhelming workouts, which cause an oxygen debt.