The phrase "to change the table" means to reverse or shift the existing situation or dynamics in a particular scenario. It suggests altering the usual roles or power dynamics to create a different outcome or perspective. Full definition
Despite this complaint, we got to know that most customers willingly recommended this crib with changing table combo to others who were planning to buy one for their baby. (babieslounge.com)
Well, one dad isn't satisfied with a lack of changing tables in men's bathrooms so he did something about it. (thenextfamily.com)
Something that can make the whole experience much easier is getting a good diaper changing table for your nursery. (momtricks.com)