Christians often underestimate the danger of incorrect teaching. Paul was well aware of its power and made sure the Galatians understood how dangerous it was.
In Gal 5:9 Paul uses a short, pithy statement to describe in no uncertain terms the danger in which the Galatians find themselves because of the false teaching of his opponents which they had at least flirted with and at most accepted. The statement itself is not difficult to understand: “A little yeast leavens all the dough.” This speaks to common knowledge about the role of yeast in baking: Even though the amount of yeast used in bread is small, it thoroughly affects the entire batch. The point of the image is to restrict the Galatians from compartmentalizing the teaching of his opponents and to warn them of its powerful effects. Presumably the Galatians could have thought, or been taught, that this teaching did not affect in any substantial way their standing before God. It was only a single matter of behavior or covenant sign which needed to be obeyed but did not substantially change their relationship to Abraham, Christ, or God. Paul refuses to allow anything like that thinking to stand. The small matter of requiring circumcision has a deleterious effect on everything, thus the initial teaching, however small or insignificant on the surface, must be decidedly rejected.
Although Paul does not state this, surely he must have in mind the way the Jews in Antioch and even Barnabas were persuaded away from the truth because of Peter’s behavior (see Gal 2:13). This would have been a real, painful example of the infectious nature of the opponents’ teaching. Paul wanted to warn the Galatians away from that terrible effect in no uncertain terms.
This is a helpful caution in contemporary times: Believers must stand against all false teaching counter to the gospel of Christ in all arenas which we influence. Otherwise we consign ourselves to its infectious power and harmful effects.