Why is the Son of God called the Eternal Father in the book of Alma?

The Father and the Son, a Doctrinal Exposition by the First Presidency and the Twelve Apostles, can be considered both authoritative and current teaching.

This exposition presents four senses in which the God is called the Father. 1) "Father" as literal parent. 2) "Father" as creator 3) Jesus Christ the “Father” of Those Who Abide in His Gospel 4) Jesus Christ the “Father” by Divine Investiture of Authority. The scripture given in Alma, along with others, is cited as supporting the second sense. The fourth sense gives most of the LDS interpretation of New Testament passages regarding the Oneness of the Trinity.

From the Book of Mormon Student manual:

Sometimes the scriptures refer to Jesus Christ by using the title “Father.” Elder M. Russell Ballard explained why Jesus Christ is sometimes referred to as both the Father and the Son:

“How can Jesus Christ be both the Father and the Son? It really isn’t as complicated as it sounds. Though He is the Son of God, He is the head of the Church, which is the family of believers. When we are spiritually born again, we are adopted into His family. He becomes our Father or leader. …

“In no way does this doctrine denigrate the role of God the Father. Rather, we believe it enhances our understanding of the role of God the Son, our Savior, Jesus Christ. God our Heavenly Father is the Father of our spirits; we speak of God the Son as the Father of the righteous. He is regarded as the ‘Father’ because of the relationship between Him and those who accept His gospel, thereby becoming heirs of eternal life. And the third member of the Godhead, God the Holy Ghost, has the specific mission to teach and to testify of truth as it pertains to the divinity of both God the Father and God the Son” (“Building Bridges of Understanding,” Ensign, June 1998, 66–67). •

On June 30, 1916, under the leadership of President Joseph F. Smith, the Brethren set forth a detailed statement on the Father and the Son entitled “The Father and the Son: A Doctrinal Exposition by the First Presidency and the Quorum of the Twelve Apostles.” A portion of this exposition explains how Jesus Christ is identified in the scriptures as both the “Son” and at times as the “Father”:

“‘Father’ as Creator. … Scriptures that refer to God in any way as the Father of the heavens and the earth are to be understood as signifying that God is the Maker, the Organizer, the Creator of the heavens and the earth.

“With this meaning, as the context shows in every case, Jehovah, who is Jesus Christ the Son of Elohim, is called ‘the Father,’ and even ‘the very Eternal Father of heaven and of earth’ [see Ether 4:7; Alma 11:38–39; Mosiah 15:4; 16:15]. …

“Jesus Christ the ‘Father’ of Those Who Abide in His Gospel. [Another] sense in which Jesus Christ is regarded as the ‘Father’ has reference to the relationship between Him and those who accept His gospel and thereby become heirs of eternal life. …

“To His faithful servants in the present dispensation the Lord has said, ‘Fear not, little children, for you are mine, and I have overcome the world, and you are of them that my Father hath given me’ (D&C 50:41). …

“Jesus Christ the ‘Father’ by Divine Investiture of Authority. … Jesus the Son has represented and yet represents Elohim His Father in power and authority. … Thus the Father placed His name upon the Son; and Jesus Christ spoke and ministered in and through the Father’s name; and so far as power, authority, and godship are concerned His words and acts were and are those of the Father” (“The Father and The Son,” Ensign, Apr. 2002, 14–15, 17).

In Summary: Jesus is the Father in three ways. 1) As the Creator. 2) As an heir to the Father for those who abide in His gospel. 3) Through divine investiture.

He was using the words of the prophet Abinadi from years earlier in Mosiah 15:

1 And now Abinadi said unto them: I would that ye should understand that God himself shall come down among the children of men, and shall redeem his people.

2 And because he dwelleth in flesh he shall be called the Son of God, and having subjected the flesh to the will of the Father, being the Father and the Son—

3 The Father, because he was conceived by the power of God; and the Son, because of the flesh; thus becoming the Father and Son—

4 And they are one God, yea, the very Eternal Father of heaven and of earth.

5 And thus the flesh becoming subject to the Spirit, or the Son to the Father, being one God, suffereth temptation, and yieldeth not to the temptation, but suffereth himself to be mocked, and scourged, and cast out, and disowned by his people.

Jesus Christ is "the very Eternal Father of heaven and of earth" because He created them (Hebrews 1:1-2). He is the Father of physical creation. (Incidentally, but out of the scope of this answer, there is great and interesting symbolism in Abinadi using the term "one God" to describe them.)

Though Book of Mormon prophets sometimes call Christ the Eternal Father, it's less commonly done today, perhaps because the distinction between Father and Son is important in LDS theology, so as to stand out from the diverse ways the Godhead/Trinity is interpreted across so many Christian denominations.