If hydrogen bonds are chemical bonds, and these bonds are broken when water changes phases, why doesn't this classify as a "chemical" change?
You must realize that the line between physical and chemical properties is very thin. Most bonds work via the same principle, which has mostly to do with electronegativity. When looked at in reactions it has probably also to do with the according entropy and enthalpy change. Hydrogenbonds are basically bonds based on electronegative attraction between two atoms (which is a simplified few of the reality). A phase change basically when a certain energy point has been reached: since heating op a substance is equal to giving it more kinetic energy (since heat is the same as the movement of individual atoms or molecules). When you reach a certain heat there is too much kinetic energy to form hydrogenbonds the same way it as it did before it changed phase. You probably can agree that molecules or atoms moving quickly is an obvious physical property. When you look at great detail to how hydrogenbonds work, it has something in common with many other way of two objects attracting each other (for example: the formula for the gravitional force between to large heavenly bodies, is very similar to the formula for the electrical force between an electron and a nucleus). 

In simple: Many of these chemical properties seem very physical when you look at them in detail. So saying that a certain property should actually be chemical because the changing of this property seems to correspond with the changing of chemical bonds, is not a realistic claim looking at how "physical"/physic based these "chemical" bonds are.