At the rate humans have gone paperless, at some point in time it is bound to become a paperless society. Paperless transactions are more eco-friendly, efficient, and can be instantaneous. Eventually paper will not be able to keep up with the flow of paperless traffic and humans will all shift over.
The tangibility of historical texts is important, preserving it as digits is not going to keep the authenticity of it. Furthermore there is no need to obscure a resource for writing. Especially in areas that have no source for electricity paper is bound to be a necessity again. Paper may also keep us bonded to nature as it is part of the trees.
There's always going to be someone out there who just can't let go of the past or who just generally likes the "old", "outdated" or "traditional" ways. Although I believe eventually the majority of humanity will have a paperless society, there'll always be a small section that retains the ways of the past.
The chances are humans ever becoming a completely paper free society are extremely low. People love having actual paper copies of things. Although Kindles and Kobos are popular, people still love books, people love to have something they can actually touch and handle. A love letter just wouldn't be the same if it was sent by email!
While I heavily advocate the use of computers in daily life, I don't believe we will ever have a truly paperless society, purely for the fact that it isn't safe. Computer data can become corrupted, servers can be hacked, and people who don't understand how a computer works could simply delete the wrong things, leaving months, maybe years of important documents lost if hard copies aren't available.
No, humans will never have a completely paperless society. Although the Internet and electronic advances have made paper use less prevalent, some paper will always exist. It would be folly for society to rely exclusively on electronic records. If world events made electronic copies of documents inaccessible or unusable, paper back-up copies offer valuable protection against disaster.