It's actually untrue that women get custody more then men. When men ask for custody, they are more likely to receive it than be denied. More often than not, they're not asking for custody.

There's a lot of reasons for that that would take a very long time to untangle properly.

As for testicular cancer being underfunded, perhaps it's because women's groups, cancer survivors, and the like have done a lot of campainging for it and pushed it into the lime light? In Australia, there's a great deal of attention paid to prostate and testicular cancer, because men worked to make it so. Just like women worked to make breast cancer important.