Simmering debates leading to polarization are observed in many domains. Although empirical findings show a strong correlation between this phenomenon and modularity of a social network, still little is known about the actual mechanisms driving communities to conflicting opinions. In this paper, we used an agent-based model to check if the polarization may be induced by a competition between two types of social response: conformity and anticonformity. The proposed model builds on the q-voter model (Castellano et al. 2009b) and uses a double-clique topology in order to capture segmentation of a community. Our results indicate that the interplay between intra-clique conformity and inter-clique anticonformity may indeed lead to a polarized state of the entire system. We have found a dynamic phase transition controlled by the fraction $L$ of cross-links between cliques. In the regime of small values of $L$ system is able to reach the total positive consensus. If the values of $L$ are large enough, anticonformity takes over and the system always ends up in a polarized stated. Putting it the other way around, the segmentation of the network is not a sufficient condition for the polarization to appear. A suitable level of antagonistic interactions between segments is namely required to arrive at a polarized steady state within our model.