Because that is June and the 16th is a grad night the parks will close early. You will loose about 3 hours of park time on that day. The park will still run full entertainment as normal for June. Fireworks, F! and WoC will just happen earlier to finish for the early close.
The reasoning why the 15-17th are the best days is this. New attraction are opening in June. AP can only try them on certain days, so they go on 13 and 14th. This shifts attendance to those weekdays away from the blocked days. Don't take this the wrong way, it's summer, new attractions. This doesn't mean 15-17 will be quiet, just better.