I agree absolutely! If we do not share memories, our learning is restricted solely to our own experiences, we can never really know another person fully, and we will not be able to easily experience empathy or other forms of emotional growth. These are purposes the sharing of memory serve on an individual basis, and they become more powerful when embodied as the memories of a tribe, a community, of a culture.
While we learn many things through our own hands-on experiences, if the memories of others are not shared, we are forced to reinvent the wheel in many instances. A quite practical example is a memory of having a bad meal at a particular restaurant. This comes to mind because yesterday, someone shared with me exactly such a memory. Now, I am unlikely to go to that restaurant because that memory was shared. This is a trivial example, of course, but we fare better relying on the memories of others than we usually realize, to repair something, for directions to a new place, for knowledge about an experience we have not had.
We are our memories, to a large degree, and if these are not shared, we cannot know another person. A few years ago, I made a new friend, and as we got to know one another, I noticed that in addition to talking about the present and the future, we both had a natural tendency to share memories, which was a powerful way to get to know one another, to understand how the other had come to be in the present. This is a human need to share ourselves.
Without the sharing of memories, we have no way of gaining insight into others, no way to develop empathy, which is also a part of being a human being. We cannot live as social beings very well without empathy. Sharing memories also serves to validate all emotions, to help us understand we are not alone in the universe, feeling things that no one else feels. When memories are shared, emotions are shared. How many times have we felt reassured about ourselves, listening to the story of a friend?
On another level, the collective memories of a group, large or small, are its culture, an embodiment of its customs, its knowledge, its arts, and its religion. Without the memories of the elders in a group, culture is lost, and on a greater scale, so is civilization.
Whether one is examing memories on a micro or macro level, they are a human imperative, and their repression is dysfunctional, as The Giver makes clear.
it really just depends. some memories are very personal. those you might want to keep to yourself. other memories might benifit others if they knew about them. they could learn from your mistakes, and get great advice. especialy if they are younger than you. for example: if your little brother is going into middle school, you might want to share your memory of your first day. it might help comfort him.
Hope this helped!