Jonas wishes he was The Giver’s son or grandson. Jonas longs for a real family, where he can love and be loved. This is why he asks his parents if they love him, and why he leaves with Gabriel when he finds out Gabe is scheduled to be released by his father. Jonas begins to consider The Giver his family, and it is likely that they are related.
After Jonas experiences the memory of grandparents, he learns above love. Love does not exist in the community, because it and all other strong emotions are stamped out by Sameness. It is no coincidence that The Giver shows Jonas the memory of grandparents. The Giver considers himself a grandfather to Jonas, and he considered Rosemary his daughter. The Giver loves Jonas, and wants Jonas to experience love.
Jonas does learn to love, and this is why he runs away. When he asks his parents if they love him and they chide him for imprecise language, he realizes that things will never change in the community unless something drastic occurs. He discusses with The Giver that it is important for them (Jonas and The Giver) to change the others, because they do not know any better. They need to be rescued from their lack of humanity.