This sort of question has been asked on this site before and I was partly satisfied with the answer here (How does centering the data get rid of the intercept in regression and PCA?)
where the images show that without the demeaning we might have our principal component not necessarily along the direction of maximum variance of our dataset. With that thread, I am still unclear as to why the principle component need to pass through the origin.
My other question is that I have seen comments to the affect that if the data is not demeaned before applying PCA, the first principle component will be the mean itself. Again, it is not clear to me why that should be the case and also why that is a problem exactly.