This is a controversial issue. But as an amateur linguist and moderately accomplished polyglot who has watched the controversy go back and forth for several decades and observed children grow up who were raised in both environments, my opinion is that the benefits of teaching a child as many languages as possible at as early an age as possible far outweigh the risks.
The way you think is largely shaped by the language(s) at your disposal. With the obvious exceptions of musicians, other artists, mathematicians, etc., the vast majority of our important thoughts are formed in words. Languages and cultures evolve together so the language you speak reflects the philosophy and world view of your community, and therefore you have no choice but to unconsciously think the way your ancestors thought.
Learning a different language is like traveling to a different planet. You find ideas in your head that could not by any means have occupied that space before, because you did not have the vocabulary, grammar, and syntax to express them. Studying Chinese, a language quite distant from English with no gender, tense, or number, which expresses relationships using an unlimited number of nouns and verbs rather than a Stone Age paradigm of prepositions and conjunctions, opened my mind up to whole new ways of perceiving reality and a whole new way of dreaming.
It also made it crystal clear to me why the Chinese have such a tremendous advantage over us in their ability to adapt to new ideas. If they can recover from the ravages of communism and overpopulation, they will once again be the Center Country and the rest of us will be the Outside Countries.
I can only imagine what it would have been like to have been exposed to Chinese when I was a baby or even a few years older, before all the synapses in my speech center had been formed, before my brain slowed down and ceased being able to absorb new concepts so quickly.
I was lucky enough to live in a place where Spanish was a mandatory course in the seventh grade. Even though Spanish is very closely related to English (compared to Algonquin, Japanese, Bantu, Arabic, or Samoan) the differences are still so profound that I spent most of that year running ideas through my head in one language and trying to see how they might change in the other.
After looking hungrily into German and Portuguese (boa tarde, meu amigo), exposure to a language from the other, eastern, branch of the Indo-European family (Russian) was a shock. Even though Spanish and Portuguese are closely related, as are English and German, the difference between the Romance and Teutonic languages was overwhelming. I thought I knew all about different ways of expressing thoughts. Russian quickly disabused me of that notion.
When I finally got to study Chinese, a non-Indo-European language, I was ready to be shown new ways of thinking that I could not have imagined, and still I was overwhelmed.
To get back to my sad point... My dear mother was a native speaker of Bohemian, or Czech as we now try to call it with our handicapped American tongues. She could have raised me speaking both languages. But my father would have none of it. He was afraid I would grow up speaking English with a Czech accent like she did. The notion that having absolutely everyone else in my life be a native speaker of English just might balance that out didn't occur to him, or to a lot of other English-first chauvinists. I also kind of think he didn't want my mother and me to be able to carry on conversations he couldn't understand.
Czech is closely related to and very similar to Russian, arguably even closer than Spanish and Portuguese. I could have had the experience I had in college sixteen or seventeen years earlier.
I can't imagine how different my life would be today if I had learned more than one language from birth. Maybe I would be a professional linguist, or a translator, or an interpreter, or a foreign language teacher, or someone who bridges gaps between nations. Or maybe I would just be a far wiser person because of my ability to have so many more different kinds of ideas in my head. Or maybe I would just be happier because the world would be easier to understand.
In any case, my life would be better.
Do your kid a favor and let him learn every language he comes in contact with!
Boa sorte.