Handling missing data is one of the most fundamental problems in machine learning. Among many approaches, the simplest and most intuitive way is zero imputation, which treats the value of a missing entry simply as zero. However, many studies have experimentally confirmed that zero imputation results in suboptimal performances in training neural networks. Yet, none of the existing work has explained what brings such performance degradations. In this paper, we introduce the variable sparsity problem (VSP), which describes a phenomenon where the output of a predictive model largely varies with respect to the rate of missingness in the given input, and show that it adversarially affects the model performance. We first theoretically analyze this phenomenon and propose a simple yet effective technique to handle missingness, which we refer to as Sparsity Normalization (SN), that directly targets and resolves the VSP. We further experimentally validate SN on diverse benchmark datasets, to show that debiasing the effect of input-level sparsity improves the performance and stabilizes the training of neural networks.