There are plenty of reasons, why you should learn a new language. Some are more obvious than others. I don't want to go into the neurological part too deeply - for simplicity let's just assume, that learning something new benefits your brain. New neuronal connections are established. The neurons connect into clusters. New 'thinking-patterns' are established, as you learn new words, grammatics and sentences.
As I write this, I'm using latin letters.
In this sentence, all latin expressions are italic, to demonstrate it's importance and relevance.
Spanish, French, Portugese, Italian are all 'romanic' languages.
With a good background in latin, you will have easy acces to these languages and can probably understand most newspaper articles. ( French not so much, to be honest )
You could be able to spot all latin expressions and have a much better understanding of English.
You will understand certain concepts to the bone and not just learn their meaning from secondary sources.
Some examples:
When you progress in latin and apply it frequently, you will soon automatically pick up on old greek, too.
Those are the two main sources of all 'philosophical' and 'political' expressions for the whole of Europe.
For a conclusion I'd like to go back to the beginning and remind you how learning languages affects your brain.
The soul becomes dyed with the color of its thoughts.
Marcus Aurelius
You could be able to think like a roman !