The study of ancient languages helps scholars understand the societies that relied on those languages. Understanding ancient societies gives contemporaries an understanding of the history of humanity. The study of the history of humanity gives society in general a better appreciation as to where we came from and how we developed.
Studying ancient cultures lends meaning and context to the world we live in today. Not only does it help us understand and prevent the repetition of pass follies, it helps us the learn empathy, respect, and the importance and value of inherent human dignity. Studying these ancient cultures is entirely dependent upon scholarly study of the ancient languages that shaped and were shaped by those cultures.
Yes, the study of ancient languages is still important today. Studying ancient languages provides students a way to understand how the languages they speak today came into existence. These languages can also provide insights into the societies and cultures in which they were used. This will in turn help students understand their own societies.
You need to know your past to prepare for the future. By studying ancient languages today, we get to know about the past through manuscripts and other text. Ancient languages gives us insight into the creation of philosophies and religions. It also gives us insights on the development of language and science theories to discover how we got where we are today.