Recent studies have shown that Large Vision-Language Models (VLMs) tend to neglect image content and over-rely on language-model priors, resulting in errors in visually grounded tasks and hallucinations. We hypothesize that this issue arises because existing VLMs are not explicitly trained to generate texts that are accurately grounded in fine-grained image details. To enhance visual feedback during VLM training, we propose S-VCO (Symmetrical Visual Contrastive Optimization), a novel finetuning objective that steers the model toward capturing important visual details and aligning them with corresponding text tokens. To further facilitate this detailed alignment, we introduce MVC, a paired image-text dataset built by automatically filtering and augmenting visual counterfactual data to challenge the model with hard contrastive cases involving Minimal Visual Contrasts. Experiments show that our method consistently improves VLM performance across diverse benchmarks covering various abilities and domains, achieving up to a 22% reduction in hallucinations, and significant gains in vision-centric and general tasks. Notably, these improvements become increasingly pronounced in benchmarks with higher visual dependency. In short, S-VCO offers a significant enhancement of VLM's visually-dependent task performance while retaining or even improving the model's general abilities. We opensource our code at https://s-vco.github.io/