Does the first son of Aadam, may Allah exalt his mention, share the sin of every murderer?

Question

What is the rationale behind the Hadeeth (narration) of the Prophet  sallallaahu  `alayhi  wa  sallam ( may  Allah exalt his mention ) that the first son of Aadam (Adam), may Allah exalt his mention, shares with every killer the guilt of the crime? Is this similar to the concept of original sin in Christianity where the person is responsible for a sin he did not commit? Or is it a different case since the first son of Aadam, may Allah exalt his mention, was the first perpetrator of this crime?   
Fatwa
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, is His Slave and Messenger.
The Prophet  sallallaahu  `alayhi  wa  sallam ( may  Allah exalt his mention ) pointed out in the Hadeeth which was narrated by Al-Bukhari and Muslim that the first son of Aadam, may Allah exalt his mention, takes part in the sin of every person who kills another person unjustly, because he was the first person to commit the act of killing.
There is a Hadeeth on the authority of Jareer, may Allah be pleased with him, in which the Prophet  sallallaahu  `alayhi  wa  sallam ( may  Allah exalt his mention ) pointed out that anyone who is the first to do a good deed and thereafter people follow his example, he will gain a reward for doing the deed and the reward for all those who follow him until the Day of Resurrection. Similarly, anyone who is the first to do a bad deed and people follow him, he bears this action’s sin and the sins of those who follow him until the Day of Resurrection. [Muslim: Saheeh]
Starting a bad deed falls into two categories:
1. A bad deed that did not exist before and was started by a person. If the doer of this deed does not repent, he will share the sin with everyone else who does that deed after him. The case of Qaabeel (Cain) belongs in this category because he did not repent of his crime. Allah the Almighty Says (what means), {So he killed him and became among the losers} [Quran 5:30]
Ibn ‘Abbaas, may Allah be pleased with him, explained that in the verse in which Allah the Exalted Says about Qaabeel (what means): {And he became of the regretful} [Quran 5:31], regret was not out of repentance. Rather, he regretted the action because he lost his brother, not because he killed him and committed a sin. Also, it was said that he regretted this because he carried the corpse of his brother for a long time, not knowing what to do with it, and when he saw a crow scratching the ground to show him how to hide the corpse of his brother, he regretted the fatigue he suffered from carrying it.
Anyone who repents from doing a bad deed will not carry the sins of those who follow him. Aadam, may Allah exalt his mention, was the first human being to breach the order of Allah The Almighty by eating from what He had forbidden him to eat. However, by consensus, Aadam, may Allah exalt his mention, does not share the sin of anyone who eats forbidden things because he repented of his sin and Allah the Almighty accepted his repentance. Thus, he became like someone who had not committed any sin.
2. The second category of beginning the perpetration of a bad deed is to reveal a sin that was hidden, or was revealed but people followed the example of the one who committed it. In such a case, that person will carry the sins of those who follow him unless he repents of the sin. Therefore, one of the righteous predecessors said that he preferred to be a follower in truth than a leader in falsehood.
By the same token, anyone who invents something new in religion, such as religious innovations, whims, etc., does an unjust act that did not exist before, or revives it and people follow him in doing it, whether he had the intention to be followed or not, will be burdened by the sins of those who follow him until the Day of Resurrection, unless he repents. Allah the Almighty Says (what means): {Because of that, We decreed upon the Children of Israa’eel (Israel) that whoever kills a soul unless for a soul or for corruption [done] in the land -- it is as if he had slain mankind entirely. And whoever saves one -- it is as if he had saved mankind entirely} [Quran 5:32]
Accordingly, anyone who kills another without a legitimate reason, be it in terms of legal retribution or a punishment for spreading mischief, then he will be regarded as killing the whole of mankind because all the souls before Allah the Almighty are equal in this regard. Similarly, anyone who saves a soul from being killed, by abstaining from killing and believing in the prohibition on killing others unjustly, will be regarded as if he has spared the whole of mankind. Abu Hurayrah, may Allah be pleased with him, narrated that he went to ‘Uthmaan, may Allah be pleased with him, on the day he was killed, telling him that he had come to support him and protect him from murderers. ‘Uthmaan, may Allah be pleased with him, asked him to depart because if he killed a person, it would be as if he killed all of mankind. 
It is not true that there is a similarity between this rule and the Christian concept of original sin. Christians say that ‘Eesa (Jesus), may Allah exalt his mention, expiated the sin of Aadam, may Allah exalt his mention. This is nonsense because how could a person be responsible for the sin committed by another while he was not, by any means, the cause of it? As for the first son of Aadam, may Allah exalt his mention, he shares the sin of every killer even if he had not intended to be followed in his wrongdoing.
We supplicate Allah the Almighty to guide us to the truth for He guides whom He wills to the straight path. 
And Allah knows best.

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