The provided resources offer a clear and consistent teaching on the Catholic Church's stance on loving one's enemies, as exemplified in the words of Jesus in Luke 6:27-31. Here is a summary of the key points:

1. Jesus commands his followers to love their enemies, do good to those who hate them, bless those who curse them, and pray for those who mistreat them (Luke 6:27-28; 1, 2).

2. This teaching is a hallmark of Jesus' message and the power of the Christian mission. It reflects God's unconditional love for all people, even those who reject him (Luke 6:27-31; 1, 2).

3. The duty to love one's enemies extends to all, regardless of how they think or act differently. This love is incompatible with hatred of the person, but not with hatred of the evil they do (Luke 6:27-31; 3).

4. Forgiveness of offenses is a key part of this teaching. Christians are called to forgive those who have wronged them, just as God forgives us (Luke 6:27-31; 4).

5. Loving one's enemies is a challenge, but it is the heart of the Gospel. It reflects the "extremism of charity" that Jesus demands, going beyond human standards of justice (Luke 6:27-31; 2).

6. Practicing this love, even in the face of painful historical events, is essential for the future of humanity. Hatred must not prevail, as love always brings victory (Luke 6:27-31; 5).

In summary, the Catholic Church's teaching, based on the words of Jesus in Luke 6:27-31, is that Christians are called to love their enemies, do good to them, and forgive them, reflecting God's own unconditional love and the power of the Gospel message.