Why must all conditions except the independent variable be held constant for all experimental treatments?

Uhm ... I believe you mean a situation when we examine a relation between two variables. In this case all other conditions must remain as constant as possible because they could affect a result and then the conclusions could be false. ie. you examine a relation between temperature and frequency of cell division/organism's activity, then you should stabilize air pressure, food composition, bacterial flora in experimental room ... etc. of course when you conduct research in a field, ie. ecological research you can't do any of that but then you are obliged to explain possible aberrations of your results in an article's discussion.