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I believe the bible is inerrant, infallible Word of God because the Bible tells me that it was indeed written by man but was "God-breathed" meaning it is the inspired Word of God. "(2 Timothy 3:16-17)All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness, so that the man of God may be thoroughly equipped for every good work" . Also, some critics of the Bible say it is simply a collection of man's writings. Others believe it is a great "literary masterpiece," but not the "Word of God." Those are the people who do not believe there is a God. Others believe God's Word is in the Bible but that the entire Bible is not God's Word. However, scholars have proven that the Bible is accurate in its depiction of historical events that have been documented elsewhere, so the rest of it should be considered true as well, in spite of the critics. On the other hand, even if none of the Bible had any secular evidence, we still should believe it rather than the world's knowledge, because it is the Word of God and is reliable.
I don't understand what the problem is with the accounts of Jesus' birth between Matthew and Luke. Both of these books were written by different men but there is nothing that is totally different. One book may not have all the facts of the other but it doesn't make it wrong or different to where if you believe one account you can't believe the other. The bible is to be taken figuratively and Proverbs 13:24 does not mean to literally beat your child to a pulp but to discipline him. Just as you, as a parent, will discipline your child (I hope) because you love him and know what is best for him.