Well, I've always disagreed with your stance about being "respectful" to your parents by not exercising your political conscience, but I agree that the whole point of petitions (as the term is usually meant) is a public endorsement of the petition statement.

That said, I don't see it necessarily as a matter of justice -- we could have secret petitions or open petitions, either way, just so long as everyone knows what the rules are, and society can work OK. I think. I'm open to arguments either way.