Many of my acquaintances are into German, Russian or French, but I do not consider it an asset unless I'll be relocating to these countries.
I don't think you get that much exposure to another culture just by learning their language, if you aren't also interacting with that other culture. I'm not saying that you don't learn anything, just that it's a very inefficient way of broadening your perspectives. For most people it takes a lot of effort to get to the point where you can have meaningful conversations in a foreign language. And if you speak English fluently, it can be a battle sometimes getting people to speak their language with you when they want to practice English or don't want to deal with non-native speakers of their language. So even I sometimes I feel like learning the language provided little practical use.
If someone has the opportunity to learn a language and then live in that country for a little while, I believe that is a very worthwhile experience. But it's not something that everyone has the opportunity to do.
My intuition is that language learning has other positive effects than just the practical one of allowing you to converse with other people in that language. For instance you say that math would be more rewarding in the long run. But why? Most people really don't have a practical need for math past arithmetic. But your intuition is that it is nonetheless rewarding. I strongly agree! But I think the same is true of language learning, for very similar reasons.
But I don't really know if my intuition is right. Maybe someone else here has a better answer.
I'm a native English speaker who learned French to a conversational level (~B2 in the European Language Framework) before I left my home country. That language skill helped me get a job where I am now. The country I am in is multilingual, so the ability to learn languages and a willingness to make an effort with other languages is very important.
I can however understand this attitude, especially if you don't travel enough to warrant it and don't really need to use it. I feel sad typing this, because I am personally very interested in languages, but language skills in my home country aren't particularly valuable or desired and English dominates. If you decide to dedicate that time to learning a different skill, well I can't really fault that.
However I'd make some observations. Firstly, knowing some words even if you travel infrequently can be helpful. Secondly, according to wikipedia, 12% of the US speak Spanish, 29% in California. That's not nothing.
As to the benefits, I personally think there are numerous. People say you "understand the culture" or something but I'm not sure you get this unless you immerse in a native-speaking country. What you get on a purely linguistic level is an understanding of grammar, an understanding of some word roots (especially if you learn French, which had a significant influence on English as a result of the Normal invasion, or Latin. Similar benefits probably exist if you learn other romance languages or maybe German/Dutch), and an understanding of how that language influences how the speakers approach the world. Also, if you ever want to help a non-native speaker improve their English, it very much helps to appreciate the struggles they're going through.
Since this is HN, I don't think my language skills have improved my programming at all. I don't like duolingo.
Learning languages helps you with all of the things you'd prefer doing. I don't know anyone who studies comparative (or increasingly, American) politics without knowing at least a second language and ideally more. Learning other languages helps with knowing your own, or at least it did for me. Knowing languages clearly helps with knowing cultures, and that helps with socializing -- it's amazing what an ice breaker even, like, two weeks of training in a language is when you meet someone who speaks it. I've found multilingual fluency has helped me with coding as well.
Most immersion during language learning is essentially passive. Instead of reading the news or watching TV in your native language, do it in the language you're learning. Very little additional investment, huge reward.
As someone who has studied a handfull of languages and have no talent for language learning I would agree. If you have no connection to the language and no desire to travel to a place where it's spoken, it would be like any other hobby. But if you want to get to know a culture in depth or work in another country it's pretty much mandatory.
This has implications beyond just communications. Many of us tend to think about things on a global scale. But when you learn another language, especially from a different language group such as Chinese/Arabic/Russian/etc, you'll find that our views and values tend to be very different than people in other nations. I mean I think we all intuitively realize this, but there's a difference between realizing something and actually seeing and experiencing it - such as by participating in discussion sites in a different language. How can we speak of ideas on a global scale with so generally little knowledge of the rest of the world? Suffice to say that our stereotypes of other nations (from which one might hope to at least glean some insight) tend to be no more accurate or insightful than foreign stereotypes of Americans!
The web is also rapidly reflecting this difference in language. The internet was 'born and raised' English, but non-English usage on the web (which currently makes up about 45% of the internet) has been growing far faster than English usage. Probably to be expected as English is likely near saturation, but it doesn't change the point that we're going to be trending downward for the foreseeable future on the internet. And perhaps far down if English's role as the 'global language' does not persist. By speaking only English you restrict yourself not only to a small slice of the real world, but what will also be an ever shrinking slice of the digital world.
And finally there are the typical arguments. Many other nations have incredibly rich cultures and histories. And these can all be unlocked with little more than the learning of a language. I'm not even really talking about books or arts from hundreds of years ago. This change and cultural difference is ongoing - movies, games, television, etc somehow have such a sharply different feel between nations. In the process of seeing these differences, you also simultaneously learn more about yourself and how your own experience has shaped who you are - which can also help you try to see things more impartially.
English is the defacto international language nowadays. I am Bulgarian, and after crossing the border with neighbouring Romania I'm using English, since the effort to learn Romanian is not worth the time when my intentions are just to travel there occasionally. The two languages are very different, and Romanians aren't willing to learn Bulgarian either.
I'm learning Italian right now since I live in an Italian speaking country, but I would probably recommend Spanish or French if you want to pick a language with more geographical diversity.