Why do they track genetic mutations, or changes, back on the mother's line?

Because Mitochondrial DNA, unlike nuclear DNA, is inherited from the mother, while nuclear DNA is inherited from both parents.

… because an egg is a cell with mDNA in it, and the egg forms the zygote, while the sperm just combines its nuclear DNA to the egg.

Only a woman can have a kid – and she can be impregnated by any number of men (and some do exactly that!).

The woman is the constant in the heredity equation. Men are interchangeable.