"Then the Emperor has already won."
Ok, rant time:
Obi-Wan completely understands the position Luke is in here because, as this gifset emphasizes, he’s been in the exact same position. He was given the same task: to kill Anakin. He too protested out of love and loyalty to family (because Obi-Wan and Anakin were family, don’t ever think otherwise). And in spite of his best efforts to carry out his duty as a Jedi, when it came down to it, Obi-Wan really could not do it. He defeated Anakin, but he could not kill him - he could not bring himself to end his brother’s life.
And so Anakin survived, and continued to serve the Emperor. He helped to kill, enslave, and oppress countless beings. He hunted down and killed the last of the Jedi who had escaped Order 66. He killed Obi-Wan himself. The consequences of Obi-Wan’s failure to kill Anakin when he was supposed to were catastrophic, and he knows it.
Now Luke is faced with the same dilemma. So when Obi-Wan tells him that the Emperor has already won if he can’t kill his father, he’s not being insensitive to Luke’s emotional struggle. He’s speaking from experience. His insistence that Luke must kill Anakin is born not of a disregard for the difficulty or gravity of that task, but of an all too personal understanding of the alternative.