Can the recycled paper's quality as good as the new one? Why?

Answer 1

Besides Caveman's answer, quality on a paper is not only measured by whiteness and purity, but by the amount of groundwood fiber.
These depend on the quality of the celluloid fibers. These fibers are what is extracted from trees. With each cycle of use, reuse and recycling, more fibers are damaged. That is why with each recycling step the paper has lower quality. This is dealt with by mixing different qualities of paper.
>They are designated as Paper Stock Industries (PSI) No. 1 Soft Mixed Paper and PSI No. 2 Mixed Paper.The primary difference in these grades is that No. 2 Mixed Paper contains less than 10% groundwood fiber.

Answer 2

Recycled paper is made from a mixture of different quality papers with loads of ink and other contaminates. Therefore it starts out as low quality because good quality is achieved by carefully controlling the paper pulp source.

There is an option to clean the recycled paper using detergents during the manufacture process but this adds cost and pollutes the environment, both of which go against the reason for using recycle in the first place.