Christians, why is Cain not in Adam’s genealogy (Genesis 5:1) ... nor

[David G]

Adam in Cain’s genealogy (Genesis 4:17)
In Matthew 13, Christ interprets the Parable of the Sower for His disciples. His interpretation documents that the devil planted his seed in the world.

Matthew 13:37-39:

37 He answered and said unto them, He that soweth the good seed (children, offspring) is the Son of man (Christ);

38 The field is the world; the good seed are the children of the kingdom; but the tares are the children of the wicked one (satan);
39 The enemy that sowed them is the devil; the harvest is the end of the world; and the reapers are the angels.

With the above in mind, it's not too surprising that Cain, Satan's son, was the first murderer.
In John, Christ further documents that Satan planted his evil seed in the world. That's why the Kenites, offspring of Cain, in the verses below, wanted to murder Christ.
John 8:38-44:

38 I speak that which I have seen with my Father (God): and ye do that which ye have seen with your father (satan).

39 They answered and said unto him, Abraham is our father. Jesus saith unto them, If ye were Abraham's children, ye would do the works of Abraham.

40 But now ye seek to kill me, a man that hath told you the truth, which I have heard of God: this did not Abraham.
41 Ye do the deeds of your father. Then said they to him, We be not born of fornication; we have one Father, even God.

42 Jesus said unto them, If God were your Father, ye would love me: for I proceeded forth and came from God; neither came I of myself, but he sent me.

43 Why do ye not understand my speech? even because ye cannot hear my word.

44 Ye are of your father the devil, and the lusts of your father ye will do. He was a murderer from the beginning (now, who was the first murderer?), and abode not in the truth, because there is no truth in him. When he speaketh a lie, he speaketh of his own: for he is a liar, and the father of it.

[KiraJenLove]

They didn't follow Cain's geneology; all his offspring died in the Flood. Since Abel was dead, they traced the ancestry of Christ through Seth, Adam and Eve's next child. Only Noah and his family, who was a descendant of Seth, survived into the post-Flood world.