Panel 1: Since Liz and Proto-Anthony Patrick are probably at the "hate each others' guts" phase of Twoo Wuv, we find her deliberately violating the "NO HORSEPLAY" rule by splashing him with water.
Panel 2: He retaliates.
Panel 3: The male counselor comes over and blows a whistle because of that no horseplay thing I mentioned.
Panel 4: Liz and Patrick stare daggers at one another and thought-bubble "Darn. Just when I was winning" at the same time.
Summary: My guess is that Lynn subscribes to the destructive and stupid belief that children use violence in order to mask affection. If she'd kept track of names better, "Anthony/Patrick" would be all about the being too much of a kid to say how he really felt.