And why should anyone believe that all Christian doctrine is explicitly contained in Scripture?
For three reasons.
The canon is closed.
Hebrews 1..
1
In many ways and in various ways of old, God having spoken to the fathers in the prophets;
2
in these last days He spoke to us in the Son, whom He appointed heir of all things; through whom He indeed made the ages;
3
who being the shining splendor of His glory, and the express image of His essence, and bearing up all things by the Word of His power, having made purification of our sins through Himself, He sat down on the right of the Majesty on high,
4
having become so much better than the angels, as much as He has inherited a name more excellent beyond them.
Scripture's authority is from God
The Scripture's authority is from being the very Word of God. God in effect wrote the Bible and it is received as God’s Word to mankind. The authority is of God not any church or person on earth (see 2 Pet. 1:19, 21, 2 Tim. 3:16, 1 John 5:9, 1 Thess. 2:13).
Scripture contains all that man needs for salvation
The whole counsel of God concerning all things necessary for His own glory, man’s salvation, faith and life, is either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture and to which nothing at any time is to be added to the now closed canon, whether by so-called
new revelations of the Spirit or traditions of men. (see 2 Tim. 3:15-17, Gal. 1:8-9, 2 Thess. 2:2).
There are
no passages in Scripture that can be extracted to prove that there is any other doctrine explicitly taught concerning another competent source
beside Scripture to convey the specific elements (all things necessary for God's own glory, man’s salvation, faith and life) to make one "
wise for salvation through faith in Christ" and to render the man of God "
complete, thoroughly equipped for every good work."
That said, no one should deny that the inward illumination of the Holy Spirit is necessary for the saving understanding of such things as are revealed in Scripture (see John 6:45, 1 Cor. 2:9-12). Moreover there are some circumstances concerning the
worship of God, and
government of the Church, common to human actions and societies, which are to be set out by knowledge that comes from creation, providence to man ("the light of nature"), and good Christian prudence, all according to the general rules of Scripture, which are always to be observed (see 1 Cor. 11:13-14, 1 Cor. 14:26, 40).
It is true that all things in Scripture are not all equally plain in and of themselves, nor equally clear to all persons (see 2 Pet. 3:16). Yet those things which are necessary to be known, believed, and observed
for salvation, are clearly presented, and opened in some place of Scripture or other, that not only the educated, but also the poorly educated, using ordinary means, may achieve a sufficient understanding of them (see Ps. 119:105, 130).
AMR