B-cell receptor signaling in response to membrane-bound antigen increases with antigen affinity, a process known as affinity discrimination. We use computational modeling to show that B-cell affinity discrimination requires that kinetic proofreading predominate over serial engagement. We find that if B-cell receptors become signaling-capable immediately upon antigen binding, which results in decreasing serial engagement as affinity increases, then increasing affinity can lead to weaker signaling. Rather, antigen must stay bound to B-cell receptors for a threshold time of several seconds before becoming signaling-capable, a process similar to kinetic proofreading. This process overcomes the loss in serial engagement due to increasing antigen affinity, and replicates the monotonic increase in B-cell signaling with increasing affinity that has been observed in B-cell activation experiments. This finding matches well with the experimentally observed time (∼20 s) required for the B-cell receptor signaling domains to undergo antigen and lipid raft-mediated conformational changes that lead to Src-family kinase recruitment. We hypothesize that the physical basis for a threshold time of antigen binding might lie in the formation timescale of B-cell receptor dimers. The time required for dimer formation decreases with increasing antigen affinity, thereby resulting in shorter threshold antigen binding times as affinity increases. Such an affinity-dependent kinetic proofreading requirement results in affinity discrimination very similar to that observed in biological experiments. B-cell affinity discrimination is critical to the process of affinity maturation and the production of high-affinity antibodies, and thus our results have important implications in applications such as vaccine design.