Why the disbeliever disbelieves in the Doomsday and the Judgment Day
The reason is to allow for himself ungodliness and indecency and transgression.. thinking there will be no judgment and no requital.
Quran 75: 5-6, which means:
(5. But man [who denies the sending of souls to the Hereafter] aims [from his denial] to go on as a profligate. 6. He questions [with denial]: "When will Doomsday take place!?")