Why does drinking milk lead to increased fractures?

Question

Milk has always been associated with strong bones due to the high amount of protein and calcium in it. Yet reading it up on wikipedia,

A study published in The BMJ that followed more than 45,000 men and 61,000 women in Sweden age 39 and older had similar results. Milk consumption in adults was associated with no protection for men, and an increased risk of fractures in women. The risk of any bone fracture increased 16 percent in women who drank three or more glasses daily, and the risk of a broken hip increased 60 percent. It was also associated with an increased risk of death in both sexes.

My question is:

Why did this happen? Can someone explain the biological reason of this observation?

Even though milk really does provide large amount of calcium and proteins yet isn't is contradictory that the fracture rates increase?

This is the aforementioned study.

Michaëlsson, K.; et al. (2014). "Milk intake and risk of mortality and fractures in women and men: cohort studies". The BMJ. 349: g6015. doi:10.1136/bmj.g6015.

Answer 1

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.