This makes total sense but its interesting, I've heard of the concept of "gifts" in like a Pentecostal sense where Christians are more or less capable of filling certain roles (pastor, teacher, prophet etc.) but evangelism wasn't seen as a gift but rather something everyone HAD to do, and they had to do it loudly. Is this a religious mandate or an artifact of some protestant cultures?
The sending of missionaries has a long tradition in Christianity that goes back to the Apostles, which is why there exist a number of well-known historic missionaries such as St. Patrick, as well as Sts. Cyril and Methodius (known as "the Apostles to the Slavs", Cyril gives his name to the Cyrillic alphabet still used today), St. Boniface, etc. But, rather consistently, Christian missionaries have been either ordained clergy or monastics (for example, Francis Xavier). And so engaging in what were, basically, perceived as apostolic missions to introduce the Gospel to other people involved individuals who had a great amount of formal theological training.
Protestant missions became somewhat pronounced in the 19th century, Presbyterians especially. The efforts of Presbyterian missionary activity in some places can still be keenly felt, for example I believe Presbyterianism is still the largest branch of Christianity in South Korea. So Protestants engaged in missionary activity just as Catholics and Orthodox had done earlier, though I believe missionaries were still usually ordained clergy rather than lay missionaries.
In the early 19th century there occurred among American Baptists something called the missions controversy, namely a split erupted among Baptists on the issue of missions--should missionaries be sent nor no? It resulted in Missionary Baptists on one end and Primitive Baptists on the other; part of the issue involved theological disputes already present within the Baptist tradition along the Calvinist-Arminian divide.
So far this is largely missionary activity, the idea of introducing the Gospel to parts of the world which were, until then, unfamiliar with the Christian religion.
If we rewind a bit to the 18th century we have the First Great Awakening in Britain and colonial America, representing what might be described as the earliest layer of revivalistic ideas. John Wesley, the founder of Methodism, though an Anglican priest had been deeply influenced by an encounter with a group of Moravians; a splinter group from Lutheranism which ascribed, largely, to Pietism which orthodox Lutherans had staunchly rejected.
In the 19th century another wave of revival took over America, and as I've mentioned in other places one of the leading figures of the Second Great Awakening was Charles Finney. I'd argue Finney really needs to be credited for the idea of finding measures to use in preaching in order to sway people's emotions to get them to make a public confession of faith. It was Finney who came up with the Anxious Bench, which came to later be called the Altar Call.
Out of the Second Great Awakening we see an explosion in what we might call popular preaching, it was also often joined together with social progressives. These early Evangelicals believed that changes in society were part of Christian mission, for example the abolition of slavery, woman's suffrage, etc. So, to their credit, these were the kinds of Christians who were more likely to be advocating for the poor, for minorities, for women, while Mainline Protestants were often against progressive social change. It's kind of funny how things change with time.
Another result of the Second Great Awakening involved an increase vigor for the sending of missionaries, in publishing religious pamphlets, etc. For example the Jehovah's Witnesses got their start with Charles Taze Russel's Bible Student Movement and the Zion's Watchtower Bible and Tract Society.
And the early-mid 20th century saw the rise of a number of popular evangelists such as Billy Sunday, and later Billy Graham; and thus the birth of the Neo-Evangelical movement.
This is largely a bunch of disjointed historical statements; but I'd say that herein we can perhaps see how the idea of every Christian supposed to being an evangelist finds its place as a growing idea from within particular niche corners of American (and British) Protestantism--specifically revivalistic/pietistic forms.
Because it's not as though Mainline Protestants, Catholics, and Orthodox don't encourage individuals to share their faith, it's just that it's not regarded as The Most Important Thing(TM), and the form in which sharing one's faith takes is quite different. There is no Lutheran or Orthodox equivalent to the "Four Spiritual Laws" (at least that I'm aware of). Both from "conservative" Lutherans and "liberal" Lutherans that I've heard speak on the issue there is a general agreement that sharing one's faith is pretty much, "If someone is curious, share" with a larger focus on actually understanding and growing in one's faith. As it usually helps to have an idea about what it is you do believe before trying to tell other people what you believe.
-CryptoLutheran