Martin Luther's primary objections seem to be:
- Most of the impediments to marriage that the Pope condemns (earlier in the sermon) are works of Papistry
- The command in Genesis to be "fruitful and multiply" trump Paul's relative assignments
- The body is made for marriage. In other words, Paul is correct when he says "It is better to marry than to burn"
- There's nothing wrong in growing the church the old fashioned way (i.e by birthing it) (Ironic, now that Catholics are the ones typically known for large families)
- It's not that celibacy is bad - it's just that its a gift that God doesn't give to all. As such, it need not be a requirement.
The key points come towards the end of his sermon "The Estate of Marriage." He says:
It is certainly a fact that he who refuses to marry must fall into immorality. How could it be otherwise, since God has created man and woman to produce seed and to multiply? Why should one not forestall immorality by means of marriage? For if special grace does not exempt a person, his nature must and will compel him to produce seed and to multiply. If this does not occur within marriage, how else can it occur except in fornication or secret sins? But, they say, suppose I am neither married nor immoral, and force myself to remain continent? Do you not hear that restraint is impossible without the special grace? For God's word does not admit of restraint; neither does it lie when it says, “Be fruitful and multiply” [Gen. 1:28]. You can neither escape nor restrain yourself from being fruitful and multiplying; it is God's ordinance and takes its course.
Physicians are not amiss when they say: If this natural function is forcibly restrained it necessarily strikes into the flesh and blood and becomes a poison, whence the body becomes unhealthy, enervated, sweaty, and foul-smelling. That which should have issued in fruitfulness and propagation has to be absorbed within the body itself. Unless there is terrific hunger or immense labour or the supreme grace, the body cannot take it; it necessarily becomes unhealthy and sickly. Hence, we see how weak and sickly barren women are. Those who are fruitful, however, are healthier, cleanlier, and happier. And even if they bear themselves weary, or ultimately bear themselves out that does not hurt. Let them bear themselves out. This is the purpose for which they exist. It is better to have a brief life with good health than a long life in ill health.
But the greatest good in married life, that which makes all suffering and labour worth while, is that God grants offspring and commands that they be brought up to worship and serve him. In all the world this is the noblest and most precious work, because to God there can be nothing dearer than the salvation of souls. Now since we are all duty bound to suffer death, if need be, that we might bring a single soul to God, you can see how rich the estate of marriage is in good works. God has entrusted to its bosom souls begotten of its own body, on whom it can lavish all manner of Christian works. Most certainly father and mother are apostles, bishops, and priests to their children, for it is they who make them acquainted with the gospel. In short, there is no greater or nobler authority on earth than that of parents over their children, for this authority is both spiritual and temporal. whoever teaches the gospel to another is truly his apostle and bishop. Mitre and staff and great estates indeed produce idols, but teaching the gospel produces apostles and bishops. See therefore how good and great is God's work and ordinance!
Here I will let the matter rest and leave to others the task of searching out further benefits and advantages of the estate of marriage. My purpose was only to enumerate those which a Christian can have for conducting his married life in a Christian way, so that, as Solomon says, he may find his wife in the sight of God and obtain favour from the Lord [Prov. 18:22].
In saying this I do not wish to disparage virginity, or entice anyone away from virginity into marriage. Let each one act as he is able, and as he feels it has been given to him by God. I simply wanted to check those scandalmongers who place marriage so far beneath virginity that they dare to say: Even if the children should become holy (I Cor. 7:14], celibacy would still be better. One should not regard any estate as better in the sight of God than the estate of marriage. In a worldly sense celibacy is probably better, since it has fewer cares and anxieties. This is true, however, not for its own sake but in order that the celibate may better be able to preach and care for God's word, as St Paul says in I Corinthians 7 [:32-34]. It is God's word and the preaching which make celibacy, such as that of Christ and of Paul, better than the estate of marriage. In itself, however, the celibate life is far inferior.
I focus on Martin Luther, because he was so adamantly against the practice of denying priests the ability to marry. It was, in part, a protest when he married Catherine, and from what I remember, she sort of signed up for it. Many of the other Protestant theologians were really just following Lither's lead on the matter.