Quick explanation: ripping your own CDs is perfectly legal. I'm actually re-ripping my entire CD collection to --alt-preset standard, and did a little research out of curiosity. Just having your own MP3s on your computer is perfectly safe, and if they're not in a shared folder on a network or on the internet, no one but you will know you have them. In this case, Tristy, your dad is right, but you have nothing to worry about, anyway. Ripping MP3s from your own CDs is well within U.S. personal use laws.
Torrenting, however, as well as DLing from an non-secure location can expose your IP to people who are gathering evidence. In the practical sense, though, no one will care or notice unless you're DLing/sharing on a massive scale or on a network that's been well compromised (like Kazaa/Grokster).