Qualifications
While there are construction management degree programs that would teach you the difference between Soil A and Soil B, what you really need to get started on this career track is experience in the construction industry—at least five years of it. You'll need to learn how to do teardowns safely, how to use jackhammers and other equipment, how to handle hazardous materials, and (hopefully) how to manage a crew.
There are various licenses and certifications you may be required to earn as a demolition contractor. There's a hazardous material removal license, which Uncle Sam makes you earn through the Occupational Safety and Health Administration (OSHA). You'll need a license to open a business as well, if you decide to go that route (source).
And that's not including the permits you'll need from your local governing body to actually carry out any demolition work.
If you want the end-all and be-all of your career to involve blowing up old infrastructure, you're going to need to sign on to an apprenticeship program, where you'll learn the ins and outs of explosives and discover that blowing up a skyscraper is way different than, say, blowing up a mountain to make way for a highway.