1. The purpose of loving enemies – To save souls (Mt 5:44)
    Lev 19:34, Isa 49:6, Lk 23:34, Mt 22:10, Acts 7:59-60, 1 Pt 3:9-15

Jesus told us to love our enemies and to pray for them. (Mt 5:44)

Mt 5:44 But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you;

The Old Testament tells us not to hate the Gentiles. The reason is that God has a plan to save those Gentiles. (Lev 19:34, Isa 49:6)

Lev 19:34 But the stranger that dwelleth with you shall be unto you as one born among you, and thou shalt love him as thyself; for ye were strangers in the land of Egypt: I am the Lord your God.

Isa 49:6 And he said, It is a light thing that thou shouldest be my servant to raise up the tribes of Jacob, and to restore the preserved of Israel: I will also give thee for a light to the Gentiles, that thou mayest be my salvation unto the end of the earth.

When Jesus was crucified, He prayed to God to forgive those who killed Him. (Lk 23:34)

Lk 23:34 Then said Jesus, Father, forgive them; for they know not what they do. And they parted his raiment, and cast lots.

Jesus explained the banquet of salvation in heaven with parables, and told them to invite both the good and the bad to the banquet. (Mt 22:10)

Mt 22:10 So those servants went out into the highways, and gathered together all as many as they found, both bad and good: and the wedding was furnished with guests.

Even Stephen, who was killed while preaching the gospel, prayed that those who killed him would be saved. (Acts 7:60)

Acts 7:59 And they stoned Stephen, calling upon God, and saying, Lord Jesus, receive my spirit.
60 And he kneeled down, and cried with a loud voice, Lord, lay not this sin to their charge. And when he had said this, he fell asleep.

Peter told us not to repay evil for evil, but to pray that they might be saved. After all, the reason we must love our enemies is so that they can be saved. (2 Pt 3:9-15)

1 Pt 3:9 Not rendering evil for evil, or railing for railing: but contrariwise blessing; knowing that ye are thereunto called, that ye should inherit a blessing.
10 For he that will love life, and see good days, let him refrain his tongue from evil, and his lips that they speak no guile:
11 Let him eschew evil, and do good; let him seek peace, and ensue it.
12 For the eyes of the Lord are over the righteous, and his ears are open unto their prayers: but the face of the Lord is against them that do evil.
13 And who is he that will harm you, if ye be followers of that which is good?
14 But and if ye suffer for righteousness’ sake, happy are ye: and be not afraid of their terror, neither be troubled;
15 But sanctify the Lord God in your hearts: and be ready always to give an answer to every man that asketh you a reason of the hope that is in you with meekness and fear: