Can a Muslim say 'brother' to a Christian or a Jew? Is it permissible according to Islam to consider them brothers?

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, sallallahu ‘alayhi wa sallam, is His slave and Messenger.

A Muslim does not address a non-Muslim as 'brother' unless he is his biological brother from his mother or father or both. If this is not the case, then he does not address him as his brother. It is impermissible to consider Jews and Christians as our brothers; rather, it is incumbent to hate them for the sake of Allah and believe that they are on Kufr (disbelief), and it is prohibited to take them as allies or incline towards them. Allah, The Exalted, says (what means): {The believers are but brothers...} [Quran 49:10]

Shaykh Ibn ‘Uthaymeen wrote, "There is never brotherhood between Muslims and Christians. True brotherhood in Islam is based on faith (Eemaan); Allah, The Exalted, says (what means): {The believers are but brothers...} [Quran 49:10] ... A believer can never be the brother of a Kaafir (disbeliever) ... it is impermissible for the Muslim to describe a non-Muslim as a brother, be he a Christian, a Jew, a fire-worshiper, or an atheist ... It is prohibited to call a non-Muslim a brother under any circumstances...”

Even considering that Muslims and non-Muslims are bonded by human brotherhood in the sense that they are the sons of Aadam (Adam), then using the term 'brother' in this sense and addressing non-Muslims extensively with it is a product of this age, in which the disbelievers prevailed over the believers and thus Muslims suffered an overwhelming sense of defeatism.

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Allah knows best.