I was recently asked this and didn’t have a very clear answer.
There is one obvious answer for learning a language: you might need it to get a job, go to school, or otherwise get ahead in life. In the US, this applies to English. All languages that are learned primarily for these reasons are lingua francas and are the most widely spoken and taught languages in the world. But English is such a successful lingua franca, even in countries where other successful lingua francas are spoken, such as Chinese, French and Spanish– there are large numbers of people that use English for business and academia.
The motivation for learning/teaching a heritage language (one that someone in your family speaks, but isn’t necessarily the local lingua franca) has to go beyond the benefits that accrue to speakers of successful and widespread lingua francas.
Advantanges that go beyond “This language is useful as a lingua franca”
1. It delays the onset of Alzheimers by about 5 years.
2. Bilingual kids have a better intuitive sense for grammar.
3. Bilinguals can multitask better as tested by seeing how they perform by doing multiple tasks in a driving simulator aka performing while distracted. (Also this article has more evidence about the same ability)
4. Bilinguals solve certain non-verbal standardized tests faster than monolinguals.
The benefits don’t come from occasional use, i.e. High school French + reading an occasional menu.
Above from this NYT article
5. Bilingualism increases brain density, and more so when the 2nd language is learned early i.e. childhood vs high school or college
Ref. Web Md
6. Children who are bilingual early on can learn a third language more easily later in life. Ref This Faq.
That is the the well documented benefits I could find on the web, there might be more but there aren’t good studies for it yet, for example, it is fairly common in articles about the benefits of bilingualism to list vague benefits.