As a semi-competent learner of languages as an adult, I'd sayis pretty solidly on to something with his "yes/no" answer… But it applies much more contextually against the backdrop of "an American living in America, primarily working in a role that does not interact with Chinese clients/bosses/etc a great deal".
Basically, Chinese is a valuable asset if you think you'll ever need/want to work or live in a Chinese-speaking nation, or if you will work with Chinese speakers a great deal.
And in that light, learning Mandarin Chinese while young has numerous advantages over another popular language – it is actually a very difficult language to learn not only to speak fluently, but also to read and write, for someone whose primary language is English.
Young language students are often much quicker to pick up a second or even third language – my 3 year-old speaks Japanese better than me already, has above-average but non-stellar English, and has memorized a dozen common children's songs in both, plus Chinese! Oh yeah, and now that she's talking non-stop, her sign language is going to hell. Kids.
If I had to make a solid recommendation based on overall usefulness/life fulfillment, I'd recommend learning English, plus 1-2 languages that use a significantly different alphabet (cyrillic, Arabic, character-based, etc) as a child.
Not to knock French or Spanish, for example, but both have lots of English-friendly cognates – due to the flow of history, both have deposited large quantities of their language into our own, and in turn all our American ingenuity has imbued these older languages with new words mostly based on things we've invented in the last 100 years[*]. Because of this, learning such languages as an adult is far easier for those with the desire to learn and no fear of looking stupid when they start speaking like an infant in some public market in Central America.
Similarly, once you've learned, say, Chinese reading and writing, Japanese will also prove a much easier target to defeat – all you'll need to punish yourself with is a very Yoda-Spanish like grammar, and general vocabulary… But the reading and writing will be merely annoying, rather than mind-numbingly difficult.
Still, above all else, remember this: kids start out loving to learn, and the best way to cure that is to force things on them that not only take away from their general play time, but also never get to "show off" – at least with something like violin lessons, when they finally complete a recital, they start to understand how cool it is to be good at something. It doesn't make much sense to start your kindergartener in Chinese if you aren't also willing to commit to trips to China/HK/Taiwan, and/or otherwise immerse your child in the language on a regular basis at home.
It's far more interesting for a child to learn the language of a parent, uncle, grandparent, cousin, etc. And if none exists… Well, music is an even more universal language than English, and can even be a far more useful skill when you're stuck in a country and don't speak a word of the native tongue.
[* In fact, the French got so mad about this trend, they made a law banning the use of such words, in favor of more "natively French" ones! http://en.wikipedia.org/wiki/Tou… ]