An ecomonics question: Equity vs. debt

Business schools have been preaching that equity is equivalent to debt. I'm not an economist, so perhaps I shouldn't venture into this debate, but I can't avoid strong feelings on this. Equity is not equivalent to debt. They have distinctly different consequences. (Edit: See a more expert contradicting argument below. Not a surprise. As I said, perhaps I shouldn't venture into this.)

Equity doesn't drive you into bankruptcy or foreclosure.

If there's an equivalent disadvantage in equity, I hope someone will tell me what it is. However, I wonder what could be equivalent, since bankruptcy can be existential crisis that leads to the extinction of a business. Can equity end a business? Can equity force a foreclosure? I don't see how.

I know about "opportunity cost" and how debt can allow you to take advantage of promising opportunities, but that's not equivalent to the danger of bankruptcy. I'm open to an explanation, but it has to be a compelling one.