I'm not an economist but I have read a lot of the MMT literature, including the available textbook (1) and it's a totally coherent framework.
Can you point me to some of those contradictions that you have observed?
(1) - https://www.amazon.com/Macroeconomics-William-Mitchell/dp/11...
https://www.amazon.com/Macroeconomics-William-Mitchell/dp/11...