What makes a two-income household a "trap" is when both parents are forced to work in order to make ends meet. This creates a nominal rise in household income that masks the actual desperation of the household's financial situation.
The trap is: declining real household income for segments of the population. The "two income" part is a consequence of the trap, not a cause.
This matters because a lot of the increasing representation of women in the workforce is not the result of the two-income trap, but the result of women, individually, wanting to work. In other words, not every two-income household is actually in a trap. Many of them are formed by two people who each have jobs they like and want to keep.
My wife, for example, has advanced training and likes her job. She couldn't wait to get back to work after we had our first child. As a family, we could survive fine on my salary today... but she would kill me if I suggested this. Now we're struggling to home-educate our child while we both work remotely. If I suggested that she quit her job to be our family's "insurance policy", again, she would kill me (even if I invoked Elizabeth Warren).
My mom worked too, because she wanted to. Good thing she did, because when my parents divorced she was able, financially, to transition to being on her own right away.
Single-income families can be a trap too... for the person who is not earning an income. About half of U.S. marriages end in divorce. A spouse with no independent financial base and no job of their own is not in a position to leave when they want to.
This stuff is really important to understand, so we don't go down a fruitless rabbit hole of wringing our collective hands about the decline of the traditional family culture or whatever. Taking that broad simple view of two-income households runs a very real risk of simply denying the agency of women who want to work and make their own way in the world... even if they are married with kids.