As it applies to relationships, it is possible to be responsible for your effect and impact on other people, without being responsible for them in their entirety. One is taking responsibility for the self which causes us to be loving towards others. One is taking responsibility for others, which causes us to be resentful towards others. Often people who 'don't want to be responsible for the happiness of others' simply don't want to be responsible for themselves; ie. the effect they have on others.