In this work we investigate critical phenomena in a variant of the chiral Gross-Neveu model and the Thirring model in 2+1 dimensions. We employ the functional renormalization group (RG), which is an extremely powerful analytical approach to describe strongly-correlated fermion systems at criticality. We compute the critical behavior of the chiral Gross-Neveu model, where we allow for a different number of left- and right-handed fermion flavors. In this sense, this system can be viewed as a toy model for the Higgs-Yukawa sector of the standard model of particle physics. The RG analysis of the Thirring model uses a full basis of fermionic four-point functions. Our results show that the UV complete (asymptotically safe) Thirring model lies in a two-dimensional coupling plane which reduces to the conventional Thirring coupling only in the strict limit of infinite flavor number. This allows for the first time a microscopic explanation for the existence of a critical flavor number above which chiral symmetry remains unbroken for arbitrary large coupling: for large flavor number, chiral symmetry breaking is prohibited due to a competition between different condensation channels. With the help of the dynamical bosonization technique we give detailed quantitative predictions for the critical behavior in terms of universal critical exponents and relate them to the literature.