For one, the ad campaign is claiming that children will be "forced" to learn about all kinds of marriage, including same-sex marriage, in schools. Apparently marriage is discussed in kids' sex-ed classes, and the argument that the proponent of Proposition 8 made was that if Proposition 8 passed, it would be "discriminatory" to talk about heterosexual marriage and not homosexual marriage (so he'd rather be discriminatory in defining marriage so narrowly?!). But parents have always had the option to opt their kids out of sex ed, so if they felt that strongly about it, they could do that. (Hell, they may even be required to sign a waiver before their kid is allowed in to sex ed -- that's how Utah works, anyway.) Also, this is such a red herring argument -- it isn't central to the issue at all.
The second argument is also both a red herring and false. The Prop. 8 proponent argued that churches that refused to perform same-sex marriages could lose their federal funding. The opponent said that there was no way for this to happen.
One of the callers mentioned the parallels between this and the fight for legalizing interracial marriage, which was "against the will of the people" in the 1950s. The proponent for Prop. 8 said that that case was completely different because interracial marriage is still "in support of families and children." (He skirted various questions around heterosexual couples who wanted to marry but didn't plan to have kids, and around homosexual couples who did have kids and wanted the legal standing to best support them that is provided through marriage.) There are also other parallels promoting various forms of segregation that were also "against the will of the people": it was equally "against the will of the [majority of] people" to do away with slavery and to integrate schools and public services in the 1950s. The rule (a.k.a. tyranny) of the majority can be dangerous: the "will of the people" isn't necessarily right, fair, or just. The California Supreme Court rightly recognized the historical and logical flaws in this argument and ruled that the civil and legal institution of marriage, or whatever you want to call it, has to have not only the same rights and benefits but the same name for all. But now that right is threatened.
So California US-citizen friends, make sure you vote NO on Proposition 8. And for everyone, Californian or no, please please please consider donating to the "No On Proposition 8" campaign to help them fight the lies.