Not all businesses fail because of unions, but let's suppose some of them did. Should the conclusion then be that we should find ways to prevent that from happening again, or should it be that two wrongs make a right?

It goes both ways. There are plenty of nations with strong unions throughout. In the US some work is primarily done by unions (such as trade work).

The fact that someone can pull up an example where a union caused a business to go under doesn't make me think "we should eliminate unions". It doesn't even make me think "We should limit union negotiation powers" primarily because unions rights have been curtailed since the Reagan era.

If you wanted to convince me to get rid of unions, you'd do it by setting up robust workers rights nationally which unions provide.