Y-DNA and the Y-Chromosome exist solely exist within men. Y-DNA is apart of our own DNA, but it’s found in the Y-chromosome of males and can ONLY be passed from father to son.

 

mtDNA, on the other hand, is the DNA of the mitochondria, and can only be passed on by women. A mother can pass the mitochondria and mtDNA on to both their female and male children, but only their daughters would then be able to pass on the mitochondria to their future children.

So, to keep things simple, men can pass along Y-Chromosomes as they only lie within men, while only women can pass on the mitochondria, but that can exist in both men and women.