All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
There is no proof indicating that every person dying sees the angels taking his soul. Some people may see them, and some may not. In a Hadeeth on the authority of Abu Hurayrah the Messenger of Allaah, sallallaahu ‘alayhi wa sallam , said that "Moosaa (Moses) saw the angel of death when he came to take his soul". [Al-Bukhari & Muslim]
The spirit of a Muslim is taken in a different way to that of a non-Muslim. The angels take the soul of non-Muslims by force. Allaah The Almighty Says (what means): {And if you could but see when the wrongdoers are in the overwhelming pangs of death while the angels extend their hands, [saying], "Discharge your souls! Today you will be awarded the punishment of [extreme] humiliation."} [Quran 6:93]
Allaah The Almighty also Says (what means): {And if you could but see when the angels take the souls of those who disbelieved. They are striking their faces and their backs and [saying], "Taste the punishment of the Burning Fire."} [Quran 8:50]
These two verses indicate that the souls of non-Muslims are forcibly removed, whereas the souls of Muslims are removed with ease. In a Hadeeth on the authority of Al-Baraa’ Ibn ‘Aazib the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, said that "the soul of a Muslim is removed like a water drop flows from a vessel. The soul of a non-Muslim is removed like a multi-pointed skewer is removed from wet wool that causes the veins and nerves to sever". [Ahmad, Abu-Daawood & Al-Haakim]
Allaah Knows best.