In response to the renewable resource argument, I would like to add the following.

It's not always clearcut whether the product made out of renewable material is better with regards to environmental issues than the non-renewable material. Take plastic bags vs. paper bags.

Paper bags are heavier and bulkier than plastic bags. Therefore, to transport the same amount of bags, more trucks are needed for the paper bags. More trucks need more fuel.

You should also take into account the energy needed for producing the bags. I don't know which process uses up more energy: the transport of wood and production of paper, or the transport of oil and the production of plastic. It might very well be that the latter process actually uses less energy. Unless the production energy is solar or wind energy, this also means less fuel used.

The same thing goes for the recyclability: both paper and plastic can be recycled. For supermarket bags the composition of the plastic is simple and well-known, making recycling easy, recycling of paper is widespread already. The trouble here is not in the recycling process itself: to recycle, people need to return their bags, or the bags need to be collected from household waste streams. The recycling process also involves transport and energy, and in this case also, plastic need not be the worst option.

In the end, it might be possible that the plastic bags, in terms of resources, are actually the better choice. Plastic bags might save more petroleum than they use up. This is not taking into account the waste problem that ensues when people just throw them away, of course.
I would like to add that, whereas I don't know whether the above story is true for bags, it certainly is true for glass milk bottles vs. plastic ones.