I say, and with Allah's success: By my life and your life, meaning your existence and life, does not require anything to be considered a violation, so it does not result in an oath. Unlike the phrase: By the life of Allah, for it is an oath, and swearing by other than Allah is disliked; as the Prophet (peace be upon him) said: "Beware! Allah forbids you to swear by your fathers. Whoever swears, let him swear by Allah or remain silent," in Sahih al-Bukhari 6: 2449. It is disliked to swear by it due to the sharing of the one swearing with Allah in glorification.