I recall an argument/debate between myself and my oldest over playing violent video games. He laid out a very logical (not manipulative) set of reasons why he should be allowed to play. At the end he stated that since I agreed with each of his statements I needed to follow the logic and allow him to play violent video games. The hitch - I told him my decision to not allow him to play was based on subjective emotion and I still felt the same way.
But yes, Zhian, in other instances if I legitimately got my pants beat in the logic game by my children I would change my stance.

Where I usually get beat is the amazing memory for things past that get thrown into the arguments.