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Animal fibres :  wool
Plant fibers:  cotton 
Artificial fibers:  polyester and many others..

Animal fibers do not dye easily. They are strong.  They protect from heat and cold.  They are expensive.  The yield or supply is less.  Availability of high quality fibers is less.  
They need space to grow animals.  They take time and effort too.
Coloring and printing on them is more difficult.
Wear and tear is less in these fibers.  However, washing needs to be done carefully with a  special procedure.
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