Right, but in so doing you're also switching the grammatical subject. The original statement assumes the same subject, moving from rights -> obligations implies a different meaning. I.e., when speaking of myself, "my rights" vs "my obligations" are very different things. Likewise when speaking of society, "our rights" vs "our obligations" also lead to a different dialog. The onus is on what we owe to others, rather than what we are owed, even though such a contract necessarily implies both.