Abraham 1

In humility, Abraham writes -

"...finding there was greater happiness and peace and rest for me, I sought for the blessings of the fathers, and the right whereunto I should be ordained to administer the same; having been myself a follower of righteousness, desiring also to be one who possessed great knowledge, and to be a greater follower of righteousness, and to possess a greater knowledge, and to be a father of many nations, a prince of peace, and desiring to receive instructions, and to keep the commandments of God, I became a rightful heir, a High Priest, holding the right belonging to the fathers."  (Pearl of Great Price | Abraham 1:2)

Obviously, he is not boasting concerning his own faithfulness, he trying to explain why and how he received the priesthood.  It is apparent that he understood that -

"...this greater priesthood administereth the gospel and holdeth the key of the mysteries of the kingdom, even the key of the knowledge of God."  (Doctrine and Covenants | Section 84:19)

Which  -

"...power and authority of the higher, or Melchizedek Priesthood, is to hold the keys of all the spiritual blessings of the church—
19  To have the privilege of receiving the mysteries of the kingdom of heaven, to have the heavens opened unto them..."  (Doctrine and Covenants | Section 107:18 - 19)

Abraham had been faithful, obedient and righteous and thus wanted to receive the mysteries of the kingdom or heaven, even the knowledge, commandments, and ordinances of God.  And he knew the only way he could receive this blessing was by obtaining the priesthood.  Thus he pursued being ordained as such so -

"I sought for mine appointment unto the Priesthood according to the appointment of God unto the fathers concerning the seed."  (Pearl of Great Price | Abraham 1:4)

The accepted pattern or "the appointment of God" was through "the fathers concerning the seed" or by fathers to their posterity.

But -

"My fathers having turned from their righteousness, and from the holy commandments which the Lord their God had given unto them, unto the worshiping of the gods of the heathen, utterly refused to hearken to my voice..."  (Pearl of Great Price | Abraham 1:5)

So

"...this Melchisedec, king of Salem, priest of the most high God, who met Abraham returning from the slaughter of the kings, and blessed him..."  (New Testament | Hebrews 7:1)

In other words, Abraham was able to get Melchizedek to give him the priesthood which was not the typical pattern -

"Which Abraham received the priesthood from Melchizedek, who received it through the lineage of his fathers, even till Noah;
15 And from Noah till Enoch, through the lineage of their fathers..."  (Doctrine and Covenants | Section 84:14 - 15)

And it was through Abraham and his seek that some of the greatest promises were given.  This should be of great consolation for those faithful saints that were preceeded by unfaithful fathers.