The relationship between Anne and Peter does not begin as an adolescent romance, though it certainly develops into one as Anne continues to write in her diary over the year and half or so that they are together in the annex.
At the beginning, Anne is not impressed with Peter who presents as a shy, lonely young boy. She observes in him a sort of laziness and passivity that she does not respect or understand. Anne is certainly a sensitive and creative young girl, as her writing shows, and she can't see why he is content to be so boring. At this early point in their relationship, they don't really have much of a connection except for the awful circumstances that have brought them together in the first place.
After some time, Anne begins to notice something different about Peter, and she concludes that he likes her in a romantic way. His interest in her seems to inspire her to reciprocate, and their relationship changes for a short time. She fantasizes about true love and marriage and wonders if Peter could be a good husband for her in the future. This burst of affection is short-lived, however, as Peter's former passivity returns, disappointing Anne, and they separate, agreeing that they will not argue with each other in the future.