I grew up in Mumbai as well. You are probably from upper-middle class, so I don't think all Mumbaikars would classify as learning English as the only language. I think you are in the minority.

I'm going off on a tangent here, but even if English is the only language you speak, it doesn't necessarily make you fluent at communicating with Americans, because you aren't necessarily exposed to the same cultural and linguistic nuances. This can often lead to a lot of miscommunication.

I have met many Indians who are fluent in English and it's the "only thing" they speak and they wear it as a badge with pride. Ironically, these people are worse than the people who are not as fluent in English because they tend to speak English at extremely high speeds as if they are reciting something, which makes it just as hard to understand. And combine that with an accent, and you've lost all the advantage you have as a "native" English speaker.