I got curious and looked it up, only because English is not my first language.
According to Wiki, "A veto, Latin for "I forbid", is the power to unilaterally stop an official action."
I take veto to mean that they have to right to tell him "No. You don't get to date this person". But it could also be used to end a relationship after it started as in "No. You can't see them anymore." Either way, too much power that I don't want