Now that you know what Modalism is, here's why it's biblically incorrect. God has revealed himself in three distinct and eternally-existent persons. In many scripture passages, we see all three interacting, an impossible and ridiculous feat if God only was one but revealing himself in three different historical ways.
Modalists take their notions from the King James Version of the Bible. Though it's a well-respected translation, the translators didn't have the wealth of scripture fragments which we have today. Consequently, Modalists mistakenly assume that their doctrines are true.
Oneness folks use Acts 2:38 as their major proof text. "Then Peter said unto them, 'Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.'" Thus, they assume only Jesus' name must be used in baptism.
Modalists also quote all the verses in the Old Testament where God says he's it and there's none else. What those folks forget is that many verses have God and the Son together. Daniel 7:13 (KJV) says, "I saw in the night visions, and, behold, one like the Son of man came with the clouds of heaven, and came to the Ancient of days, and they brought him near before him." How could the Ancient of Days and the Son of Man be in the same scene together?
Jesus often referred to himself as the Son of Man. We see that perfectly in Matthew 16:13 (KJV). "When Jesus came into the coasts of Caesarea Philippi, he asked his disciples, saying, 'Whom do men say that I the Son of man am?'"
Furthermore, we see all three members of the Trinity present at Christ's baptism. Luke 3:22 (KJV) says, "And the Holy Ghost descended in a bodily shape like a dove upon him, and a voice came from heaven, which said, Thou art my beloved Son; in thee I am well pleased." Unless God used stand-ins, this couldn't happen with a modalist deity.
I could provide many more explanations and scriptures which prove the utter impossibility of Modalism but I'll save those for my next book. We must have a proper understanding of the Trinity in order to realize the love between three distinct beings in the Godhead. Otherwise, we would worship a deity who talks to himself and is a narcissist. Nothing could be further from the truth.