Ironically, a significant part of public debt we have today still comes from the aftermath of the last private debt crisis we had: first as a (too timid) response to the 2008 banking crisis, then as the result of the economic crisis that ensued.

When an entire society is built on private debt, it doesn't matter if you don't own debt by yourself, this is a society problem, and thus it becomes your problem.

Also, unless you are super wealthy (and should be taxed more) it's unlikely that you'll stay debt-free for your entire life.