A couple reasons why they might not have included to give as an alternative is primarily because they want you to focus on not to many different meanings at the same time. Maybe also to help you pay special attention to the transitive/intransitive difference between ageru/agaru, since these are some of the first you learn (through WK).
A third reason I can think of is it’s a dangerous meaning to learn out of context. There are different words for giving and receiving in Japanese. All to do with the direction the action is going in, and the relative status of the parties involved. (This is why I wondered whether you got to chapter 24 yet, which dips into this concept).