The school isn't built like a sports arena, so traffic flow around it is fine throughout the rest of the day, but morning dropoff in particular is very congested because the volume of traffic spikes for a single 15 minute period each day.
Coupled with general morning rush hour traffic, this ripples out to long left-turn waits (no turning arrow), congestion, angry drivers trying to cut down residential streets, parking problems, and so on. Then depending on how far away you had to park, you have to walk that distance with young kids.
Pick up time is easier, especially with after school programs, because the spike is diffused out over a wider range of time.