Data observability is crucial for modern businesses as it helps maintain trust in data by addressing issues such as incorrect information and feature drift over time. Convincing stakeholders to invest in data observability can be challenging, but there are four common reasons that justify this investment: saving engineering time, increasing data team leverage, avoiding costly lapses in data quality, and preserving trust. By implementing a data observability tool, businesses can save time and money while ensuring the accuracy of their data, ultimately leading to better decision-making and improved customer satisfaction.