Of all of humanity's differing opinions concerning how things ought to be, what is to determine which course is the best way for us to live our lives? Everyone needs to agree on one ultimate Source of reference or else there will be confusion and dissention. The Bible is that Source because it is "inspired of God". There is no one better to give advice than the Creator and Designer of humans:
"All Scripture is inspired of God and beneficial for teaching, for reproving, for setting things straight, for disciplining in righteousness, that the man of God may be fully competent, completely equipped for every good work." (2 Tim. 3:16)
Jesus quoted the Scriptures because the Bible is the ultimate authority and guide on how people should live their lives. But he humbly made sure to attribute all of this wisdom to his Father:
"What I teach is not mine, but belongs to him that sent me." (John 7:16)
"Jesus said: “I do nothing of my own initiative; but just as the Father taught me I speak these things." (John 8:28)
The Bible contains the principles needed in order for us to successfully solve our problems. People may not always respect another person's OPINION, but the chances are greater that people will respect the Scriptures and Biblical principles that that person may refer to.
For more, see:
Quote that explains fascinating facts concerning Jesus' use of Scriptures (JWQ&A)
Bible
Search For Bible Truths - ARCHIVE
Scriptures Index
Search For Bible Truths - Search Guide