In the last decades, there has been a deceleration in the rates of poverty reduction, suggesting that traditional redistributive approaches to poverty mitigation could be losing effectiveness, and alternative insights to advance the number one UN Sustainable Development Goal are required. The criminalization of poor people has been denounced by several NGOs, and an increasing number of voices suggest that discrimination against the poor (a phenomenon known as \emph{aporophobia}) could be an impediment to mitigating poverty. In this paper, we present the novel Aporophobia Agent-Based Model (AABM) to provide evidence of the correlation between aporophobia and poverty computationally. We present our use case built with real-world demographic data and poverty-mitigation public policies (either enforced or under parliamentary discussion) for the city of Barcelona. We classify policies as discriminatory or non-discriminatory against the poor, with the support of specialized NGOs, and we observe the results in the AABM in terms of the impact on wealth inequality. The simulation provides evidence of the relationship between aporophobia and the increase of wealth inequality levels, paving the way for a new generation of poverty reduction policies that act on discrimination and tackle poverty as a societal problem (not only a problem of the poor).