All textiles shed and slowly release their fibres into the air. Those fibres eventually make it into your body. If they are made of a synthetic fibre, your body cannot digest it. It is important to have indoor rugs made of natural fibres so that the fibres pass through or break down within your body naturally.
Rugs made of natural fibres can actually have a positive effect on air quality because they act as a natural filter trapping all types of dust floating in the air. Just be sure to vacuum occasionally.