Here is Bruce Metzger's commentary on this verse that explains why it is left out of the United Bible Society's Greek New Testament text, which attempts to be as close to the original Greek text as possible. It is much easier to understand Bruce's commentary than the textual critical apparatus. Note that the Western Text is known for being afraid to leave out anything and its tendency to include all textual variations.
8:37 omit verse {A}
Ver. 37 is a Western addition, not found in 𝔓45, א A B C 33 81 614 vg syrp, copsa, eth, but is read, with many minor variations, by E, many minuscules, itgig, vgmss syrh with * copG67 arm. There is no reason why scribes should have omitted the material, if it had originally stood in the text. It should be noted too that τὸν Ἰησοῦν Χριστόν is not a Lukan expression.
The formula πιστεύω … Χριστόν was doubtless used by the early church in baptismal ceremonies, and may have been written in the margin of a copy of Acts. Its insertion into the text seems to have been due to the feeling that Philip would not have baptized the Ethiopian without securing a confession of faith, which needed to be expressed in the narrative. Although the earliest known New Testament manuscript that contains the words dates from the sixth century (ms. E), the tradition of the Ethiopian’s confession of faith in Christ was current as early as the latter part of the second century, for Irenaeus quotes part of it (Against Heresies, III.xii.8).
Although the passage does not appear in the late medieval manuscript on which Erasmus chiefly depended for his edition (ms. 2), it stands in the margin of another (ms. 4), from which he inserted it into his text because he “judged that it had been omitted by the carelessness of scribes (arbitror omissum librariorum incuria).”
Metzger, B. M., United Bible Societies. (1994). A textual commentary on the Greek New Testament, second edition a companion volume to the United Bible Societies’ Greek New Testament (4th rev. ed.) (pp. 315–316). London; New York: United Bible Societies.