Many bipartite networks describe systems where an edge represents a relation between a user and an item. Measuring the similarity between either users or items is the basis of memory-based collaborative filtering, a widely used method to build a recommender system with the purpose of proposing items to users. When the edges of the network are unweighted, the popular common neighbors-based approaches, allowing only positive similarity values, neglect the possibility and the effect of two users (or two items) being very dissimilar. Moreover, they underperform with respect to model-based (machine learning) approaches, although providing higher interpretability. Inspired by the functioning of Decision Trees, we propose a method to compute similarity that allows also negative values, the Sapling Similarity. The key idea is to look at how the information that a user is connected to an item influences our prior estimation of the probability that another user is connected to the same item: if it is reduced, then the similarity between the two users will be negative, otherwise, it will be positive. We show that, when used to build memory-based collaborative filtering, Sapling Similarity provides better recommendations than existing similarity metrics. Then we compare the Sapling Similarity Collaborative Filtering (SSCF, a hybrid of the item-based and the user-based) with state-of-the-art models using standard datasets. Even if SSCF depends on only one straightforward hyperparameter, it has comparable or higher recommending accuracy, and outperforms all other models on the Amazon-Book dataset, while retaining the high explainability of memory-based approaches.