The gemara discusses the validity of mila by a nochri. A posuk is mentioned about Avraham to prove that a nochri can't do mila on a Jew. I don't see what the hava amina is. Why do we need a separate posuk? A nochri can't write a sefer Torah or a get. A nochri can't make kiddush for us or read the megilla or the Torah or blow the shofar for us. A nochri is not in the parsha to be motzee us for any of our religious obligations. He's not chayav himself. In order to be motzee someone one must have the same level of obligation. A koton can't be motzee a gadol because he's not chayav in mitvos yet. A woman probably can't be motzee a man for blowing the shofar or layning. Their hischayvus is not the same. Why would we think a nochri can be motzee us in mila? Might it be a question of cheftza and gavra? We care about the results - that the baby becomes mohul, that the operation take place rather than who does it?
Samuel Kosofsky
The Chachamim here not only see a Hava Amina, but also Pasken like this l'Maseh. Regarding why, it is true that a Goy cannot be Motzi someone. However, here we are concerned about results, and the result required is that the baby be Mahul. The Teshuvos Avnei Nezer (318:7) indeed states that the father does not fulfill a Mitzva by having the Nochri do so, as there is no Shlichus by an Akum. Yet according to the Chachamim, this halachah would still be useful in order that the baby should be considered Mahul (see also Tosfos 27a, DH "v'Chi").
All the best,
Yaakov Montrose