I think this will help:
SEPARATION
According to Smith: “Sheep and goats mingle and graze together each day. But when they are moved to fresh pasture or when sheep are due for shearing or goats for milking, or when evening falls and the goats must be sheltered against night’s chill, then they are separated” [p. 297].
The word for “separate” (aphorizo) is a fairly rare word (10 times in the NT – 3 in Mt). It occurs twice in v. 32 of our text and also in 13:49: “So it will be at the end of the age. The angels will come out and separate the evil from the righteous.”
It is one of Matthew’s themes that there are sheep and goats, evil and righteous, wheat and weeds (Mt 13:24-30) in the church at the present time. The separation is not our responsibility, but the responsibility of the angels or of the king who comes at the end of the age. Although Mt does have the discipline section in ch. 18, where a church member sins against another, the purpose of the discipline is not separation, but seeking to restore the wayward one. Until the time that the angels come to do the actual separating, we may have to put up with those stupid jerks in the world (and in the church) while we pray earnestly, “Come, Lord Jesus, come.” 
SHEEP AND GOATS
Jeremias indicates that: “sheep are the more valuable animals; moreover their white colour (in distinction from the black of the goats) makes them a symbol of the righteous.” [p. 206]
I’m not sure where I picked up this idea, but I used it in a sermon on this text. Why “sheep and goats”? Why not good sheep and bad sheep or good goats and bad goats? Why two different animals? It is impossible for a goat to become a sheep.
It was common for a shepherd to have both animals in his flock. However, throughout the Bible, including the First Reading (Ezek 34:11-16, 20-24) and Psalms (100 or 95:1-7a) for Christ the King A, God’s people are referred to as sheep. Throughout scriptures the image of sheep and shepherd is used to talk about the relationship between God and God’s people. Goats are not used in the image of this relationship. 
Perhaps that the most important part of this parable: We are to be sheep under authority of the Good Shepherd. The separation takes place between sheep and goats before either group is told what they have or haven’t done. The sheep are told before they know anything about what they’ve done, “Come, you that are blessed by my Father, inherit the kingdom prepared for you from the foundation of the world.” It is not their “good deeds” that brings the blessing; it is because they are sheep, God’s people, living under authority of the Good Shepherd. But as sheep, they naturally did such good things for the needy and also to Christ. 
Reference : Brian Stoffregen ( I’m not endorsing his theological views, but I believe he did a nice job describing the significance of the sheep and the goats) 
God bless,
Aaron