This is true for at least two reasons. First, Christ and the apostles taught this doctrine. In the second place, a Bible that is not completely inerrant is hopelessly untrustworthy because no one could be sure that what he reads in the Bible is an inerrant portion. One would have to be omniscient to know which words are correct and which are not correct. Only if all Scripture is true can it be confidently read and obeyed.
Religious liberals deny the doctrine of Biblical inerrancy.
At best, they believe that Scripture is only true and trustworthy in matters of faith and practice, not in its historical, geographical, or scientifical teachings. At worst, they believe that Scripture is not even true and trustworthy in certain matters of faith and practice. According to the liberal view, God's Word is erroneous in many of its teachings and is not completely dependable. This low view of Scripture is diametrically opposed to the high view of Scripture held by the Lord Jesus Christ. Those who claim to be disciples of Christ certainly ought to hold the same high view of Scripture that He held.