I’m not sure the Pope’s opinion is actually backed up by scripture.
Start with Matthew 19. The pharisees try to trick Jesus and try to get him to weigh in on the divorce issue. The pharisees cite Moses. Jesus counters and says we must go back to the beginning - Adam and Eve, to find the true nature of marriage.
Therefore, let us look to Genesis 2:18:
The LORD God said, “It is not good for the man to be alone. I will make a helper suitable for him.”
I.e., God created marriage because being a single guy isn’t good for your long-term well being, a fact as true today as it was 4000 years ago. There is nothing about children.
Given the church’s position of married priests, there may be some cognitive dissonance going on.
For I would that all men were even as I myself.... I say therefore to the unmarried and widows, It is good for them if they abide even as I. But if they cannot contain, let them marry: for it is better to marry than to burn. — 1 Corinthians 7:7-9
It is not good for the man to be "alone" because man is an inherently social person and he needs a much broader society, a culture, a civilization. The woman is the "suitable partner" or "suitable helper" for him because together they can produce the human race, i.e. first the family, and via the family, the whole human society which now covers the earth.
So the issue is not just emotional satisfaction, sexual partnering, the companionship of a man and his mate as a couple: the issue is the procreation of a family, a society, so that the earth may abound with a splendid human civilization, a kind of mirror-image of the myriads of angels who are the citizens of heaven.
If celibacy --- singleness for the Kingdom of Hod --- were not the calling of some, Our Lord and St. Paul would not have spoken of it. It is, obviously, not for everyone: but as Jesus said (Matthew 12:19) "Those who can accept this, should accept it."
And then there is the other Genesis account of Adam and Eve where the Lord tell them to be fruitful and multiply.
-— I’m not sure the Pope’s opinion is actually backed up by scripture. -—
Pope Francis and Pope Benedict are certainly aware of the Scripture passages relevant to marriage. And you’re right. Marriage is also directed to the mutual good of the spouses.
So the purpose of a natural marriage is two-fold, the mutual good of the spouses, and the begetting and rearing of children.
The Christian marriage aims even higher. The spouses are obligated to help each other attain heaven, and so too with their children.