It is interesting that in the entire Parsha of Eliezer finding a wife for Yitzchok, it never says his name “Eliezer”; only “Eved (the slave of) Avraham”. Why did such a strange story take place with an Eved (which are known for Z’nus) that he should bring a young girl from the distance, without any concern for Inyanei Yichud, etc.? The answer is that since Avraham Avinu’s entire essence was total breaking Middos, so too the Eved (slave) of Avraham Avinu was also total breaking Middos; and breaking Middos means going extreme in the opposite direction. (Rambam).
So the Avoda of an Eved (which are known for Z'nus) is to be: פָ רוּש (abstain) completely. So there is no one more: מְסוּגָל cut-out to bring Rivka, than an Eved who would be a major: פָ רוּש abstainer and the safest person to go along. Being an “Eved Avraham” meant that every inch of him is going against his natural Tevah (nature), and nobody is better to bring Rivka.
By those who work on Middos, the calmest person is the one whose nature is to be a Ka'asan (prone to anger) but he goes extreme opposite; and the same is with all Middos.
