Why is there no genealogy of Cain?

Cain is the first born child of the human race.  He was a farmer who became the first murderer, killing his own brother Abel.

When the specific time came for the family to bring an offering we read that the Lord “did not respect Cain and his offering. And Cain was very angry, and his countenance fell” (Gen. 4:5)

“He brought the fruit of the ground and Abel of the firstlings of his flock. Cain's temper and offering (being bloodless) were not acceptable, while Abel's received the divine approval. (New Unger's Bible Dictionary) 1Jn.3:12.

Gen 4:11-12 The Lord pronounced a curse upon him and the ground that he should cultivate. Cain’s conscience would forever be stained, as the voice of his brother's blood would cry from the ground. Expelled from Eden Cain became a fugitive, (v.12) in the land of Nod, where he built a city that he named after his son Enoch. His descendants are named to the sixth generation and appear to have reached an advanced stage of civilization, being proficient in music and the arts. Yet His family line degenerated morally and spiritually becoming corrupt before God. They were wiped out in the flood.

The Bible follows the genealogy of Christ’s lineage or those significant to it. Cain is not included.

Although we have the names of only three of Adam's sons, Cain, Abel, and Seth, scripture tells us Adam had several other sons and daughters (Gen 5:4).  None of these other ones are mentioned either, only Seth. We do not make a doctrine from silence but from what is explicitly written.

The Lineage of Cain:

Irad -Runner; wild ass, one of the antediluvian patriarchs, the father of Mehujael (Gen 4:18), and grandson of Cain.

Lamech - the wild man. (1.) The fifth in descent from Cain. He was the first to violate the primeval ordinance of marriage (Gen 4:18-24). His address to his two wives, Adah and Zillah (Gen 4:23, 24) (Easton's Illustrated Dictionary)

The eldest son of Cain (Gen 4:17), who built a city east of Eden in the land of Nod, and called it "after the name of his son Enoch." This is the first "city" mentioned in Scripture.  

Methusael Champion of El; man of God, a descendant of Cain (Gen 4:18).

Gen 4:17-26 “And Cain knew his wife, and she conceived and bore Enoch. And he built a city, and called the name of the city after the name of his son-- Enoch. To Enoch was born Irad; and Irad begot Mehujael, and Mehujael begot Methushael, and Methushael begot Lamech. Then Lamech took for himself two wives: the name of one was Adah, and the name of the second was Zillah. And Adah bore Jabal. He was the father of those who dwell in tents and have livestock.        His brother's name was Jubal. He was the father of all those who play the harp and flute. And as for Zillah, she also bore Tubal-Cain, an instructor of every craftsman in bronze and iron. And the sister of Tubal-Cain was Naamah. Then Lamech said to his wives: "Adah and Zillah, hear my voice; wives of Lamech, listen to my speech! For I have killed a man for wounding me, even a young man for hurting me. If Cain shall be avenged sevenfold, then Lamech seventy-sevenfold."

Lamech is in the lineage of Cain. He became the first polygamist and the second murderer who also wanted protection from God. The man he killed had to be in his lineage for Seth was the next in Adam’s lineage which has a span of approx. 100 years after Abel.

V.25 -26 “And Adam knew his wife again, and she bore a son and named him Seth, "For God has appointed another seed for me instead of Abel, whom Cain killed." And as for Seth, to him also a son was born; and he named him Enosh. Then men began to call on the name of the LORD.”

After this Adam had his next son, who then also had a son (Enosh) being trained in righteousness -- then men began to seek God, as Cain’s seed did not during this time period.

Jared begot Enoch (Gen.5:18) who begot Methuselah it was then that Enoch was taken

Adam’s lineage the son of Jared and father of Methuselah. Gen.5:21; then his son Lamech begot Noah

Gen 5:29 And he called his name Noah, saying, "This one will comfort us concerning our work and the toil of our hands, because of the ground which the LORD has cursed." Luke 3:37 (approx 3378-3013 b.c.)

In the Epistle of Jude (1;14) Enoch is described as "the seventh from Adam;"  who prophesied of men in the end times that were like those in his day that eventually brought the flood.