Wrong. Satan is not a child of God.
This seems to be one of the most popular charges in modern anti-Mormon literature.Though Christ is the creator of this earth and our one and only Savior and is the Only Begotten of the Father in the flesh, He shares something with us in that we are all spirit sons and daughters of God (Heb. 12:9; Acts 17:28; Numbers 16:22) as is Christ (see also Hebrews 1:5,6; Heb. 2:9-12; Matt. 12:50; Col. 1:15; Psalms 89:27; Romans 8:29; Rev. 3:14). Christ differs from us in that He alone was perfect, serving as was Co-creator with God and as Savior of all mankind (all who will accept Him). Yes, technically, Satan is the brother of Christ, but so are all of us and all the angels, both good and fallen. But anti-Mormons want to make this doctrine sound scary by leaving out the information that would explain our position, and suggesting that somehow we worship a false "Mormon" Christ who is like Satan. Ugh!
It's a Biblical doctrine that Satan was in heaven originally but fell from heaven. Here is an excerpt from the article "Satan" in Smith's Bible Dictionary:
Of the nature and original state of Satan, little is revealed in Scripture. He is spoken of as a "spirit" in Ephesians 2:2; as the prince or ruler of the "demons" in Matthew 12:24-26; and as having "angels" subject to him in Matthew 25:41; Revelation 12:7, 9; The whole description of his power implies spiritual nature and spiritual influence. We conclude therefore that he was of angelic nature, a rational and spiritual creature, superhuman in power, wisdom and energy; and not only so, but an archangel, one of the "princes" of heaven. We cannot, of course, conceive that anything essentially and originally evil was created by God. We can only conjecture, therefore, that Satan is a fallen angel, who once had a time of probation, but whose condemnation is now irrevocably fixed. As to the time cause and manner of his fall Scripture tells us scarcely anything; but it describes to us distinctly the moral nature of the evil one.As for our common heritage with Christ as sons of God, the teachings of the Bible are clear. In Romans 8:14-18, I see Paul saying that our divine heritage from God is what makes it possible for humans to become "joint heirs with Christ." Though we may be potential "joint heirs," Christ is always and eternally our Savior.Latter-day Saints also believe that Satan was a spirit being in the premortal existence that we all shared, who, as Revelation 12:7-9 describes, rebelled against God and was cast down to earth, with those angels (spirits) who followed Satan (see also Jude 1:6, 2 Peter 2:4). Lucifer (Satan) was in heaven and was "a son of the morning" (Isaiah 14: 12-15) who sought to usurp God's glory and throne, rather than follow God's will (see also Job 1:6, where Satan comes into an assembly among the sons of God - these sons of God, premortal spirit children, existed before the creation of the earth was completed, according to Job 38: 4-7).
Just as we see the potential for great goodness and great evil in humans around us, so has there always been such potential among the spirit children (Heb. 12:9) of God who are blessed with liberty to choose God and Christ or to choose evil. Satan chose the greatest evil possible and still works toward that end. That he was in heaven and was a "son of the morning" among the spirit beings there ("morning stars" in Job 38:7) makes his fall and his guilt and his eternal punishment all the more terrible. But our understanding of who Satan was and is - a fallen angel, by choice a total and complete enemy to God and Christ - does not make us unchristian, in my opinion. Nor does it give us any respect for that abominable being!
Simply saying that "Mormons think Christ and Satan are brothers" is a distortion of LDS doctrine - it is deliberately misleading. We see all of humanity and all of the angels - fallen as well as divine - as creations of God, spirit sons and daughters, given freedom to choose good (through Christ) or evil. Christ is obviously a Son of God, though much more completely than we are. He is also our Savior and even our Eternal Father in several ways. Our common relationship to those who are Good and those who are truly evil in no way impugns the Good or blasphemes God and Christ.
Obviously, Latter-day Saint doctrine is not derived from the popular teachings of mainstream churches, but I see it as being in harmony with the Bible, though others are free to interpret the Bible differently. But I hope you won't mistake differences in interpretation with a rejection of Christ, to whom I look for salvation.