The Giver tells Jonas to stay away from the river for two reasons. The first reason is to protect Jonas himself. The Giver does not want to see Jonas hurt or drowned in the river.
The second reason that the Giver tells Jonas to stay away from the river is to protect the community. The Giver is the keeper of the community's memories of the past and emotions. As the Receiver, those memories and feelings are being transferred to Jonas. If Jonas were to die, all of those memories would flood back into the population of people. The people would be completely unprepared to instantly receive a year's worth of happy and painful memories. The influx would likely cause panic or massive amounts of depression. Either way, the sameness would be sorely damaged.
"You know," he said, finally, "if they lost you, with all the training you've had now, they'd have all those memories again themselves."
Jonas made a face. "They'd hate that."
"They certainly would. They wouldn't know how to deal with it at all."