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.

That's exactly my point: Changing the word that's used doesn't matter, what matters is getting people to think of others instead of themselves.

Yeah, that makes sense in egalitarian societies, but in real world societies, it means the slaves aren't allowed a voice.