I think there are two aspects to the question. First, why would he consider her to be a piece of property and second, why would he consider her to be damaged. The answers to the two are related.
He considers her to be his property because this novel is set in the late 1800s in a conservative society. In those days, women were often considered to be the property of their father or their husband.
Along with this, a wife was expected to act in certain ways. One of the themes of this work is that Edna does not behave in "correct" ways. This opening scene shows that. Mr. Pontellier thinks it's dumb to go swimming at this time (it's not what proper people do). So the tan that Edna gets while swimming shows that she acts improperly. Therefore, he considers her to be damaged --- there's this visible sign of how she has behaved "wrongly."