Why does O'Brien choose to include the story about a young girl named Linda in the book The Things They Carried?

I'm afraid your question stems from the misconception that The Things They Carried is a collection of stories only about war and warriors.  No.  The Things They Carried is about how humanity deals with death. 

If you look at the collection in this regard, the story about Linda is in the selection entitled as follows:  "The Lives of the Dead."  It is a perfect indication that the dead may not always be warriors on the army battlefield.  Yes, we are all battling SOMETHING (and in this case, Linda is battling cancer), but it doesn't have to be in the context of an army or of a war dictated by a government.  Look at the intensity of this young love here:

Linda was nine then, as I was, but we were in love...it had all the shadings and complexities of mature adult love and maybe more, because there were not yet words for it, ... I just loved her. Even then, at nine years old, I wanted to live inside her body. I wanted to melt into her bones -- that kind of love.

If you would like to bring Linda distinctly back to the title of the whole collection of The Things They Carried, O'Brien has "carried" the "thing" of Linda's memory since his childhood.  It is beautiful and, yet, it is sad:  her death from a disease as serious as cancer. O'Brien himself, then, has had to deal with what all of his characters have had to deal with:  the severity and finality of death.