It has to do with ecclesiology. Protestantism is on the whole far more individualistic than Catholicism in their view of salvation. As a result, they view things like missionary work that is the duty of the Church as extending to each member individually, so that everyone has a gospel call to personally spread the Word. Mormonism follows Protestantism in this view, which is so widely accepted now that almost no one ever notices that it is unbiblical - not in the sense that the Bible contradicts it explicitly, but it is totally absent from the Bible, and indication point in the opposite direction. In Paul’s epistles, for instance, while Paul himself is out preaching among the unconverted and asking local congregations to pray for his success, he never enjoins them to take the word to others, but is entirely concerned with how they live among themselves. He never upbraids the Corinthians, for example, for passing up opportunities to share their faith with unbelievers. The assumption that Paul takes for granted at every point is that missionary work is his own calling, and his companions’ calling, but is not a specific duty for the other members. When does write about winning souls, it only happens in those Epistles that are specifically addressed to other missionary preachers like Timothy.
Of the scant number of proof texts that people use to support the ethic of a universal missionary calling at an individual level, the most common is Matt 5:14-16:
You are the light of the world. A city set on a hill cannot be hid. Nor do men light a lamp and put it under a bushel, but on a stand, and it gives light to all in the house.Let your light so shine before men, that they may see your good works and give glory to your Father who is in heaven.
Sounds like a good verse, but look again. Is that what it is really saying? Rather it is saying that it is good in itself for me to thank God when they see the good works of Christians, no strings attached. For instance, if a starving Hindu gets a meal at a Christian soup kitchen, thanks God for the Christians’ charity, and then goes on being a Hindu, then the Christians at the kitchen have done their job.
It is important to understand this, however, in the context of the Doctrine of the Mystical Body. The body has many parts, but each part is still related to the others. If the hand cannot say to the foot “I have no need of thee,” the missionary cannot say to the nun in the convent “I have no need of thee.” Every member in the Church does participate in missionary activity by virtue of prayer, the sacraments, and whole life of grace that fuels the Church’s missionary efforts. People will convert when they meet missionaries, but the cause of their conversion is the mediation of grace that comes from the whole Church, all members involved. The missionaries do the footwork, but those nuns get them the converts.