In general, when there is this strong reaction, "Oh, that's too much suffering, I don't want to think about this any more", what that means is that this person has not done enough Dukkha reflection yet. We have to actually open our minds and hearts to see Dukkha in the world. Then when we want to do a Compassion/Lovingkindness meditation regarding Dukkha, it's easier because we've examined Dukkha specifically by itself.
The D/D method puts the two together. We're actually looking at Dukkha, and, primarily with the D/D method, it's our Dukkha, and then other people who have the same or similar Dukkha around the world. Then in the second half of the D/D method, we reflect about someone else similar to us, who can't handle that Dukkha. They have more Dukkha because of it, and more, and more, so that at the end they commit suicide, killing themselves and killing others. With the D/D method in specific, we're actually looking at exactly the same or similar Dukkha, but realizing there are many others around the world with it, and they may not have any methods with which to help themselves. So to open to Dukkha itself is important to be able to do this type of meditation properly.
If we don't want to look at Dukkha, we're missing the First Noble Truth". What's the First Noble Truth? Dukkha exists. It's just there. What do I say after I tell the "Monopoly story"? "It doesn't matter whether you like it or not. It doesn't matter whether you agree with it or not. It doesn't even matter whether you know about it or not. Dukkha is just part of life's rules. If we can understand life's rules, then we'll be able to play the game of life better."
So this is it, we have to open to Dukkha to be able to do the Compassion properly for others, whether it's in the D/D method, or the standard Compassion/Lovingkindness method.
Now for this type of person, I'd say, "Well, you have to sit down, and do more Dukkha reflection. You have to think about the body, "How can the body have Dukkha?" You have to think about the mind, "How does the mind have Dukkha?" Think about other people in the world, and just examine it objectively, without getting emotionally involved. With the Compassion/Lovingkindness meditation, we often stimulate the emotions, and get too involved, especially in the D/D method which is our personal Dukkha. But if we've done Dukkha reflection on it's own enough, objectively, then we can work better in the Compassion/Lovingkindness meditation regarding the Dukkha we're reflecting about.