Determining whether a molecule can be synthesized is crucial for many aspects of chemistry and drug discovery, allowing prioritization of experimental work and ranking molecules in de novo design tasks. Existing scoring approaches to assess synthetic feasibility struggle to extrapolate to out-of-distribution chemical spaces or fail to discriminate based on minor differences such as chirality that might be obvious to trained chemists. This work aims to address these limitations by introducing the Focused Synthesizability score~(FSscore), which learns to rank structures based on binary preferences using a graph attention network. First, a baseline trained on an extensive set of reactant-product pairs is established that subsequently is fine-tuned with expert human feedback on a chemical space of interest. Fine-tuning on focused datasets improves performance on these chemical scopes over the pre-trained model exhibiting moderate performance and generalizability. This enables distinguishing hard- from easy-to-synthesize molecules and improving the synthetic accessibility of generative model outputs. On very complex scopes with limited labels achieving satisfactory gains remains challenging. The FSscore showcases how human expert feedback can be utilized to optimize the assessment of synthetic feasibility for a variety of applications.