Well, first of all, you have to contend with the massive base of people who already speak English as a second language. More students currently study English in China alone than in the US. Add this to a strong desire for English proficiency in other East Asian countries, extremely strong penetration of English in continental Europe, and English's importance among the economic and social elite in India (soon to be even more populous than China), and you have formidable momentum on English's side. You certainly don't see millions of German schoolchildren lining up to learn Mandarin, or ambitious Indian students attending Mandarin institutions to land a plum job in an office park.
Sure, you say, but Latin and French were the "world languages" of their time—what's to stop English from suffering the same fate? Frankly, there's no equivalence. Latin and French may have been the languages of diplomacy, science, and the cosmopolitan elite in Western Europe, but they had nowhere near the worldwide prominence that English now enjoys, nor its wide base of second-language speakers of varied economic standing.
And at the same time, Chinese is hard. Yes, more people speak Mandarin or Cantonese as a first language than English, but that's not necessarily the most accurate comparison. One of the most difficult aspects of learning Chinese is the massive number of characters used for writing, which are far harder to learn than an alphabet. In fact, if we tally up the number of native speakers of languages using the Latin alphabet alone, we easily pass a billion: English, Spanish, Portuguese, German, French, Italian, Turkish, Polish, and so on. These people—and indeed almost anyone who uses an alphabet rather than a logographic script, which is the vast majority of the world—will have a far easier time reading and writing in English than Chinese. This is a particularly critical advantage in the Internet age, as it's faster and simpler to write in English characters than painstakingly hammer out the pinyin for Chinese ones.
The conclusion is inescapable: English is here to stay. Mandarin may well become the world's second most prominent language, but we English speakers will continue to unfairly benefit from stumbling into the world's lingua franca at birth—and given my limited linguistic capacity, I'm damn glad about that.
Edit: Follow-ups here and here.