Cotton is a natural fibre, it's highly absorbent and extremely strong when compared to synthetic fibres. Cotton doesn't leave scuff marks or lint on dishes and glassware.
Linen is also a highly regarded material to use for kitchen cloths and tea towels for the same reasons and is known to be a very strong material choice.
Kontex towels in particular, are hand woven on traditional, vintage Japanese looms. The looms are still used today because of how durable the structure of the weave becomes, while still keeping the cotton soft.