You are re-breathing your own carbon dioxide, which is taken into the red blood cells displacing oxygen. A local doctor was on a radio talk show recently. He put his oxygen meter on his finger, then put on a mask. In a couple of minutes his blood oxygen level went down several points. I then asked waitresses in a restaurant what they experienced after wearing their masks for a while. Many said headaches, drowsiness, and dizziness. I am an Industrial Hygienist, and I have monitored processes that used CO2. Headaches and sleepiness are common effects of over exposure.
This is most commonly seen when the A/C in a building doesn’t provide enough make-up air for the number of occupants, resulting in CO2 levels going up.
If putting a piece of cloth over your face causes any respiratory issues for you, you should seek immediate medical attention because there is something seriously wrong. Even fairly unhealthy people will have no medical problems associated with wearing a simple mask. You’d have to be at the point where you already require nonstop supplemental oxygen before you’d have any issue with a simple piece of cloth being across your face.
If these claims held any water whatsoever, people would have been collapsing and dying left and right across the world where masks have been very common for months. Lo and behold! No bodies lining the streets from mask-collapse!