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 There are a lot of mathematical theorems that you rely on in your everyday life, which may have been proved using induction, only to later find their way into engineering, and ultimately into the products that you use and on which your very life may depend. Moreover, even if you are not a mathematician but, say, a software developer, engineer, physicist or, for that matter, statistician, you may come across problems as part of your daily work where being able to find/prove a solution using induction can greatly simplify things.

Of course if your work or life's interests involve other things, it is quite possible that you will never use something like induction, ever. But even then, your life may nonetheless depend on tools that were designed or developed by people who had this (and many other "tricks of the trade") in their mathematical toolbags as they did their job.