Avraham did not say "Im Lo
Ha'Emek Davar: He wanted them to understand that if he cannot get a girl from his family, he may take from Kena'an, lest they demand an exorbitant amount for Rivkah.
Avraham did not mention 'Beis Avi' or 'Mashpachti.' Why did Eliezer say this?
Malbim (37): Her family would not understand why Avraham rejected Benos Kena'an. Is there no proper girl there?! Therefore, he said that Avraham desired from his family 1 , due to love of kin, and if not, he will take from Benos Kena'an.
Ha'Emek Davar: He wanted them to understand that l'Chatchilah, he prefers his father's house, but if not, others in his family [lest they demand an exorbitant amount for Rivkah].
Ha'Emek Davar (40): This was to help convince them that Rivkah was the one Avraham intended for.
Malbim: And really, Avraham specified only the land he came from, but never mentioned his own family.