Why were dinosaur skeletons so light compared to mammal skeletons?
I have also heard the claim that dinosaur bones were lighter than mammal bones of equivalent  size, and at the moment I do not believe it.  I will not believe it until somebody explains it to me how that is possible.  

If you have a structure that you want to add more weight to, to support that weight, you want to ADD structural elements, not subtract them.  If the structure could support itself before adding more weight, then adding structural elements will make it stronger (unless it's already at the absolute limit).  Otherwise, the structure does not stand at all. 

If you google about the weight of bird bones, you can find recent research saying that bird bones are actually not lighter than mammal bones.  Their weight is just distributed differently (more densely on the outside of the bone, as opposed to more evenly spread throughout the bone as in mammals) to resist bending and twisting better at the cost of being weaker to impacts.  Birds arguably have a much stronger reason to lose weight than dinosaurs, but their bones are still just as heavy as ours.  Since birds are dinosaurs, I find it very unlikely that ancient terrestrial dinosaurs had magic bones lighter than both mammals and birds.  

Also, I'm aware that the internal structure of our bones is very efficient.  As I understand it, the bone on the inside of a bone grows thicker where it is more stressed.  If you train a computer to calculate the ideal lattice structure to support the stresses of a given bone shape, the computer calculates pretty much the exact same lattice as what actually exists in our bones.  So, if the internal structure of our bones adapts to better handle the stresses we experience in life, and if the bones of vertebrates can evolve into any external shape whatever, I cannot imagine how dinosaur bones could be stronger than ours unless they were made of a different material.  I am not aware that this is the case.