The perceptual task of speech quality assessment (SQA) is a challenging task for machines to do. Objective SQA methods that rely on the availability of the corresponding clean reference have been the primary go-to approaches for SQA. Clearly, these methods fail in real-world scenarios where the ground truth clean references are not available. In recent years, non-intrusive methods that train neural networks to predict ratings or scores have attracted much attention, but they suffer from several shortcomings such as lack of robustness, reliance on labeled data for training and so on. In this work, we propose a new direction for speech quality assessment. Inspired by human's innate ability to compare and assess the quality of speech signals even when they have non-matching contents, we propose a novel framework that predicts a subjective relative quality score for the given speech signal with respect to any provided reference without using any subjective data. We show that neural networks trained using our framework produce scores that correlate well with subjective mean opinion scores (MOS) and are also competitive to methods such as DNSMOS, which explicitly relies on MOS from humans for training networks. Moreover, our method also provides a natural way to embed quality-related information in neural networks, which we show is helpful for downstream tasks such as speech enhancement.