Hadith: Adam denied, so his offspring denied; Adam forgot, so his offspring forgot; and Adam sinned, so his offspring sinned

عن أبي هريرة رضي الله عنه ، قال: قال رسول الله صلى الله عليه وسلم : «لما خلق اللهُ آدمَ مسح ظهره، فسقط من ظهره كل نَسَمة هو خالقها من ذُرِّيته إلى يوم القيامة، وجعل بين عيني كل إنسان منهم وَبِيصًا من نور، ثم عرضهم على آدم فقال: أي رب، مَن هؤلاء؟ قال: هؤلاء ذريتك، فرأى رجلا منهم فأعجبه وَبِيصُ ما بين عينيه، فقال: أي رب مَن هذا؟ فقال: هذا رجل من آخر الأمم من ذُرِّيتك يقال له: داود. فقال: رب كم جعلتَ عُمُرَه؟ قال: ستين سنة، قال: أي رب، زِده من عُمُري أربعين سنة. فلما قضي عمر آدم جاءه مَلَكُ الموت، فقال: أوَلَم يبقَ من عمري أربعون سنة؟ قال: أوَلَم تُعْطِها ابنَك داود قال: فجَحَدَ آدمُ فجحدت ذُرِّيتُه، ونسي آدمُ فنسيت ذُرِّيتُه، وخَطِئ آدم فخَطِئت ذُرِّيتُه».
[صحيح] - [رواه الترمذي]

Abu Hurayrah (may Allah be pleased with him) reported that the Messenger of Allah (may Allah's peace and blessings be upon him) said: "When Allah created Adam, He wiped his back and every person that He created among his offspring until the Day of Judgment fell out of his back. He placed a ray of light between the eyes of every person. Then, He showed them to Adam and he said: 'O Lord, who are these?' He said: 'These are your offspring.' Adam saw one of them whose ray between his eyes amazed him, so he said: 'O Lord, who is this?' He said: 'This is a man from the latter generations of your offspring called Dawūd.' He said: 'O Lord, how long did You make his lifespan?' He said: 'Sixty years.' He said: 'O Lord, add forty years from my life to his.' At the end of Adam's life, when the angel of death came to him, Adam said: 'Do I not have forty years remaining?' He said: 'Did you not give them to your son Dawūd?' He said: 'Adam denied, so his offspring denied; Adam forgot, so his offspring forgot; and Adam sinned, so his offspring sinned.'"
[Authentic hadith] - [Narrated by At-Termedhy]

Explanation

When Allah created Adam, He wiped his back and all his human offspring that Allah would create until the Day of Judgment came out of his back. This wiping and coming out should be understood literally, and it is not permissible to interpret it beyond the apparent meaning, as this is the methodology of Ahl As-Sunnah. When Allah took them out of his back, He placed a glimmering light between each person's eyes, then he showed them to Adam. Adam said: "O my Lord, who are these?" Allah, the Almighty, said: "They are your offspring." He saw a man among them whose light between his eyes amazed him, so he said: "O my Lord, who is this?" Allah, the Almighty, said: "He is Dawūd." Adam said: "My Lord, how long would he live?" He said: "Sixty years." Adam said: "My Lord, add forty years from my lifespan to his." When Adam had lived all his lifespan minus forty years, the angel of death came to him to take his soul. Adam said: "There are forty years remaining in my life." He said to him: "You gave them to your son Dawūd." Adam denied it because that was in the unknown world of progenies, and he did not remember it upon arrival of the angel of death. As a result, his offspring also denied. Likewise, Adam forgot, so his offspring forget; Adam disobeyed, so his offspring disobey, because the child resembles his father. Dawūd's lifespan was forty years and Allah made it sixty. Allah, may He be glorified, is All-Knowing of what happened, what will happen, and what did not happen if it happened how it would be. He knows what He wrote for him and what increase He would grant him later. The angels have no knowledge except what Allah informs them. Allah knows things before they happen and after they happen. For this reason, scholars said that erasing and affirming occur in the sheets of the angels; but knowledge of Allah, Glorified and Exalted, never changes, nor does He become aware of anything He does not know before. Therefore, there is no erasing or affirmation in His knowledge.