What's wrong with the rule? Simply put, it doesn't do enough with the information about the food. The actual food product is but one part of the pairing equation, you need to think about how it is prepared. Baking, roasting, BBQ, boiling all change the basic flavor of the food (Raw tuna and grilled tuna have different flavors and different textures). How the food is dressed needs to be taken into account as well. What spices are present in the preparation? Is the food "hot" or mild? Are there heavy sauces present? The list goes on and on...
Afraid now? Don't be. You can cut through a lot of this with some simple augmentation of the basic "red wine red meat" rule. Rather than that rule, learn these simple guidelines:
As you grow in wine you can augment and change these rules to make your own. Let's see how we can use them for a traditional Thanksgiving dinner. Here we have tart (cranberries), fatty (mashed potatoes and gravy), slightly sweet (yams with or without marshmellows), roasted fowl (turkey). What to pick? How can one wine go with all these flavors? Two very traditional picks are the Riesling (leaning toward a dryer domestic or a German Kabinett) and a Pinot Noir. You won't go wrong with these and here you have a white and a red offering. Here acidity is king and the lighter bodied, higher acid, and in the case of Pinot Noir lighter tannins make these two the wine equivalents of "universal donor". Want something a little more off the beaten path? Consider the following:
Those are the basics. You'll find some people will like more spice, more pepper and offer a Syrah while other keep the elegance flowing with a good brut sparkling wine (the exploration of sparkling wines is a joy... you will find out they go with a wide range of foods). In the end the key rule the the rule you should always follow when buying wines, that is, buy what you like and don't let anyone make snide comments about your selection. After all, you're the host and they should be gracious guests at your table.