... He blew into his nostrils the soul of life ...
Why did HaShem use nostrils instead of mouth?
PS. ISTR that, according to a midrash, the fire which killed Nadav & Avihu did so via their nostrils too, is this related?
Because the soul enters and exits the body via the nose. In the Midrash "Pirkei Rebbi Eliezer" it says that from the beginning of creation nobody became ill, but instead a person would sneeze and his soul would exit from his nostrils, until Yaakov came along and asked Hashem for mercy - that He shouldn't take his soul until he has time to command his offspring how to conduct themselves after he is dead. Hashem accepted his request, as it says Bereishis 48,1 "And it was after these things that Yosef was told: Behold! (something unusual!), your father is sick", something which had never occurred from the days of creation!
The Midrash concludes that therefore when a person sneezes one should wish him life (health) because sneezing used to signify the opposite of life. This is the source of saying Bless You or Gesundheit or לבריות or something similar in different languages.