Excellent question. The answer is that, in general, there is a higher rate of mutation in spermatogenesis compared to oogenesis. This is because there are more cell divisions during spermatogenesis, which allows for opportunities for mutation.
In addition, repeat diseases like Huntington’s sometimes have a phenomenon known as anticipation. This is when the disease gets phenotypically (and genetically) more severe with each successive generation. The exact molecular basis of this is not completely understood, but it is just well known that DNA polymerase tends to make more mistakes in large repeat regions, causing an expansion of the repeat. Anticipation is not linked to gender, I just wanted to point out that these repeats are prone to mutations that will expand the repeat and cause disease
You can see anticipation in this graph. This example is for Fragile X. The higher the repeat number in the parent, the greater the chance the child develops the disease. The parent doesnt have the disease, but what happens is the repeat mutates and gets expanded to the point where the disease will develop.
So, put these two facts together and you have your answer. A male's sperm tends to have a higher overall mutation rate, and the region responsible for Huntingtons is already prone to disease causing mutations as it is. The result ends up being the disease gets ‘inherited’ more often from the father
Picture from here