Why does drinking milk lead to increased fractures?
The authors suggest a reason in their abstract:


  Given the observational study designs with the inherent possibility of residual confounding and reverse causation phenomena, a cautious interpretation of the results is recommended.


There are variables they haven't measured that lead to the observed patterns. A simple one is that the respondees to the initial survey are self-selected (they return the survey). What if milk-drinkers are more likely to respond? Even if the base rate of fractures remains the same, then there will be an apparent association of fracture with milk consumption.

They also discuss physiological reasons, which is the subject of a different answer.