Indeed, Allah elevates some people with this Book and degrades others

This Hadīth means that the Qur'an is taken up by some people, who consequently read it. Allah elevates by means of the Qur'an some people in the world and afterlife, and demotes by means of which others in both worlds. Those who are elevated are those who follow the Qur'an, believe in its news, observe its commands and prohibitions, and take as their model the ethics it promotes.

Allah will raise their status in this world and in the Hereafter because the Qur'an is the fountainhead of knowledge. Allah, the Almighty, says: {Allah will raise those who have believed among you and those who were given knowledge, by degrees} [Sūrat al-Mujādalah: 11]. In the Hereafter, these people will be elevated in the gardens of bliss. On the other hand, the people whom Allah degrades by means of the Qur'an are those who read the Qur'an and even recite it well, but are arrogant toward it.

They neither believe in its news nor implement its rulings. They are arrogant in theory and practice. For example, when they come across stories of the previous Prophets or others, or information about the Last Day, they suspect and do not believe in them. They might even end up denying the Qur'an, although they read it. These Allah will demote in both worlds.