Ve'Avraham zaken ba bayamim - Avraham was old, advanced in days [years]
The meaning of this verse is seeing Avraham felt that he had aged he was afraid that he might die before Yitzchak had married. He did not want to send off his servant without an oath in the event he would not return from his mission before he, Avraham, had died. By making Eli'ezer swear he assured himself that Yitzchak would do what he wanted as Yitzchak was in the habit of listening to Eli'ezer's advice.
The reason that Avraham did not impose an oath on Yitzchak instead was so that the servant would not be able to fool Yitzchak by presenting any number of arguments see that he was not under oath to Avraham. Avraham considered the Kenaan as captive to deceitful practices as we know from Hoshea 12:8 "A Kenaani uses false weights, loves to overreach." He made the servant swear to reinforce Eli'ezer's obligation in the matter.