How can the Mormon Church believe that human beings can become gods?
There is no dispute that God is our Father. The appellation of Father for God is used in the scriptures more than any other term. So all mankind are the sons and daughters of God. This familial relation is not figurative, but real. God is the Father of the spirits of all mankind. As mentioned by Paul in Romans—
The Spirit itself beareth witness with our spirit, that we are the children of God:
And if children, then heirs; heirs of God, and joint-heirs with Christ; if so be that we suffer with him, that we may be also glorified together (Rom 8:16-17).
Now the question, Is there any living species in existence where the offspring do not have the potential to grow to the maturity of the parent? Simply put, men are of the race of the Gods. God, the Father, has given to his children the requirements for eternal maturation. Those requirements are called the gospel of Jesus Christ. As Paul mentions, we may become heirs of the Father if we suffer with the Savior.
Modern day revelation clearly reaffirms the biblical doctrine of the apotheosis of man, as in Doctrine & Covenant 76—
And again we bear record–for we saw and heard, and this is the testimony of the gospel of Christ concerning them who shall come forth in the resurrection of the just–
They are they who received the testimony of Jesus, and believed on his name and were baptized after the manner of his burial, being buried in the water in his name, and this according to the commandment which he has given–
That by keeping the commandments they might be washed and cleansed from all their sins, and receive the Holy Spirit by the laying on of the hands of him who is ordained and sealed unto this power;
And who overcome by faith, and are sealed by the Holy Spirit of promise, which the Father sheds forth upon all those who are just and true.
They are they who are the church of the Firstborn.
They are they into whose hands the Father has given all things–
They are they who are priests and kings, who have received of his fulness, and of his glory;
And are priests of the Most High, after the order of Melchizedek, which was after the order of Enoch, which was after the order of the Only Begotten Son.
Wherefore, as it is written, they are gods, even the sons of God– (D&C 76:50-58)
The phrase, as it is written, is a key phrase, referring to the fact that this sacred and essential doctrine of the gospel of Jesus Christ is amply documented in the Bible.
God standeth in the congregation of the mighty; he judgeth among the gods. (Psalms 82:1)
I have said, Ye are gods; and all of you are children of the most High. (Psalms 82:6)
Behold, what manner of love the Father hath bestowed upon us, that we should be called the sons of God: therefore the world knoweth us not, because it knew him not.
Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is.
And every man that hath this hope in him purifieth himself, even as he is pure (1 John 3:1-3).
Grace and peace be multiplied unto you through the knowledge of God, and of Jesus our Lord,
According as his divine power hath given unto us all things that pertain unto life and godliness, through the knowledge of him that hath called us to glory and virtue:
Whereby are given unto us exceeding great and precious promises: that by these ye might be partakers of the divine nature, having escaped the corruption that is in the world through lust. (2 Pet 1:2-4)
Let this mind be in you, which was also in Christ Jesus:
Who, being in the form of God, thought it not robbery to be equal with God. (Philip 2:5-6)
He that overcometh shall inherit all things; and I will be his God, and he shall be my son (Rev 21:7)
As an essential and crowning requirement for godhood, in addition to all the above requirements, his children must qualify to enter the holy temple as husbands and wives and there be sealed to one another for all eternity by the power of the holy priesthood. In that holy house is given the specific promise to receive the blessings of godhood, in accordance with their faithful compliance with the requirement to live a Christ-like life, as declared in D&C 132:19-20.
And again, verily I say unto you, if a man marry a wife by my word, which is my law, and by the new and everlasting covenant, and it is sealed unto them by the Holy Spirit of promise, by him who is anointed, unto whom I have appointed this power and the keys of this priesthood; and it shall be said unto them—Ye shall come forth in the first resurrection; and if it be after the first resurrection, in the next resurrection; and shall inherit thrones, kingdoms, principalities, and powers, dominions, all heights and depths—then shall it be written in the Lamb’s Book of Life, that he shall commit no murder whereby to shed innocent blood, and if ye abide in my covenant, and commit no murder whereby to shed innocent blood, it shall be done unto them in all things whatsoever my servant hath put upon them, in time, and through all eternity; and shall be of full force when they are out of the world; and they shall pass by the angels, and the gods, which are set there, to their exaltation and glory in all things, as hath been sealed upon their heads, which glory shall be a fulness and a continuation of the seeds forever and ever.
Then shall they be gods, because they have no end; therefore shall they be from everlasting to everlasting, because they continue; then shall they be above all, because all things are subject unto them. Then shall they be gods, because they have all power, and the angels are subject unto them.