14 years ago, when I was 1st learning to be a fitness trainer, one facilitator told our group that it was a "silly waste of time" to train a body part that is still sore from the last workout. He said that all you are doing is re-breaking what is trying to rebuild itself. I was only 18 and his cock-sure manner made me more-or-less take his word as gospel.
How do you all feel about this? Many bodybuilding programs I have seen call for training every other day or more.

A lot of the soreness is lactic acid buildup in the muscles. Lactic acid is an energy source so it can be used by the muscles. Also muscles will swell with fluid, stretching nerve fibers in the muscle sheaths. So Exercising while sore is not a bad thing. It mobilizes the fluid and uses up the lactate. Many
people in their 50's or 60's seem to do better with every-other-day workouts. Anyone younger can handle daily workouts. In high school we did bone-crushing workouts m-f and double workouts on Saturday.

If you're too sore to tolerate a workout, you might need a massage to work the lactate out.

Yeah, that's old information, bordering on myth. Recent studies show that the protein synthesis (growth stimulus) peaks at 24-36 hours (I forget exactly which), so waiting 48 hours between working the same muscles is probably the wisest route (so train same muscle group 2-3 times a week).

Waiting longer than that (in other words, the traditional one body part a day split) isn't optimal for growth, unless you're either genetically gifted or using assistance drugs.

Also, soreness isn't indicative of growth, just that your muscle/tendons/connective tissue were placed under unusual stress. They will adapt, and you may not get sore after awhile. So, it's ok to train when still sore.

I seperate muscle groups onto different days and hit each muscle group hard once a week, giving it plenty of time to recover.