Why do yolks break so easily (sometimes)?
Yes, the freshness is the factor. In the US eggs are sold in three grades: AA, A, and B (rare). The grading is based primarily on age. AA are the freshest, and B the oldest.

Here is a diagram depicting the internals of an egg:



The characteristics of the freshest eggs are:


A large thick albumen (white)
A small thin albumen
A sturdy thick chalaze
A small air space
A sturdy round yolk when lying flat


As the egg ages the following things happen:


Thick albumen breaks down, getting smaller
Thin albumen gets larger
Chalazae degrades getting thinner and weaker
Air space increases
Yolk membrane weakens, when cracked it lies flatter
Embryo may become visible as a red speck


As a result of the weakening membrane the yolk is indeed easier to break. Michael's suggestion to use your fingers to separate the eggs is spot on. The edge of an egg shell is a little too risky for reliable separation of eggs.