The reading from the Torah on the second day of Rosh Hashana recounts the story of the akeida [the binding of Yitzchak]. At the end of the story, Avraham is told that his brother had children whose progeny lead up to the birth of his son’s bashert, Rivka. A number of people’s names are included in that genealogy, but the name of one who is to play a major role in future events — Rivka’s older brother, Lavan — is omitted.
One possible answer is that he need not be mentioned because once the Torah arrives at Bethuel’s name, it can immediately move on to the birth of his daughter without listing his other children. But there likely is more to it than that.
There is a principle advanced in Bava Basra (110A) that one who marries a wife should check out her brother because his character foretells how her sons will turn out. Rashi quotes this in connection to Vaera 6:23 to explain why the Torah mentions the name of the brother of Aharon’s wife. In that instance, the brother was a most illustrious character, a propitious choice for the husband.
However, Rivka’s brother was a notorious rasha. Consequently, the Torah does not bring him up in connection to Rivka at the point when she is introduced as Yitzchak’s future wife. In that context, Lavan would be viewed as a reason to nix the shidduch [proposed match]. Rather, Rivka is presented without the mention of her infamous brother to be accepted in Avraham’s family on her own merits.
We can take a lesson from that in how we introduce prospective matches ourselves.