This is an old rule of thumb and one that has taken a ton of abuse over the years. The basic underlying tenet at work here, that red wines with acid and tannin work well with meats that are rich and fatty and that white wines work best with lighter fair, is sound. One thing that has changed completely since people started to discuss food and wine pairings is the food.
Today, we have so many cultural influences in the fusion that is our cuisine that it’s often easier to pair with the preparation than with the main protein. That doesn’t mean that red with meat and white with fish is off base, it’s just a relic of an earlier time. So, red wine with meat and white wine with fish remains plausible, just not as fail-safe as it might have been a few decades ago. The bottom line remains that the best food and wine pairing is the one that you enjoy most. Experiment and discover what makes you happy!