I will let you know about the more popular traditional view on the subject first, and then mention why that view is not acceptable to me. Finally you will get my understanding on the subject.
A) The Popular View
Verse 5:51 of Qur'an has been translated thus: "O believers! Take neither Jews nor Christians as your protecting friends (auliya): they are only protecting friends of one another. Whoever of you disobeys this commandment will be counted as one of them. Surely Allah does not guide the wrongdoers."
Mawlana Shabbir Ahmad Usmani mentions in his Tafsir while explaining the above-translated verse thus:
"Aulia is the plural of wali. Wali means a friend, some one close, as well as a helper. What it means is that Muslims are expected not to make Jews, Christians, and all other disbelievers (kuffar) their protecting friends, as has been clarified in surah Nisaa. However, to deal with them with justice, politeness, generosity, and decency is quite another matter. If believers feel it to be necessary, they can have agreements of peace with all disbelievers, as has been mentioned in verse 8: 61. Justice is meant to be done in case of all humans, whether Muslim or non-Muslim. The attitude of politeness and decency can be demonstrated for those non-Muslims who are not antagonistic towards Muslims. However, as far as Muwalaat (i.e. confidence of friendship and brotherly help and support) is concerned, no Muslim has a right to establish it with any non-Muslim."
B) My Reservations
I have quite a few problems when I try to rationally understand this point of view in the light of Qur'anic teachings. I will just mention a few of them here:
Qur'an allows Muslim men to marry Jew and Christian ladies: "Likewise, marriage with chaste free believing women and also chaste women among the People who were given the Book before you is made lawful for you." (5:5) It also tells believing men to be good to their wives : "Treat them with kindness even if you dislike them; it is quite possible that you dislike something in which Allah has placed much good." (4:19) It also tells us that good wives are the ones that have the following attributes: "Honorable women are, therefore, devoutly obedient and guard in the husband's absence what Allah requires them to guard (their husband's property and their own honor)." (4:34) The Almighty mentions the closeness of the husband-wife relationship in many different ways. For instance, Qur'an says: "And of His signs, another one is that He created for you mates from among yourselves that you may find comfort with them" (30: 21) He also says "They (your wives) are an apparel for you and you for them. " (2:187)