Well, you didn't say very much, I'll give you credit for that. By not saying anything relevant to the picture posted, it leaves us all to assume your position on this. Do you really want that?
Apparently, there are people who think flags should only be lowered to half-staff for the mourning of dead soldiers and recently dead presidents. These people are ignorant. These people also include the father of the Army private, who burned the American flag on his BBQ grill in protest of the flag being lowered in the state of New Jersey for Whitney Houston, a well known and liked New Jersey native and resident. Aristotle nailed it. It's not like the flag wasn't lowered when the Army private died, because it was.
When Joe Paterno died, the governor of Pennsylvania ordered the flag flown at half staff. There are far more examples of flag lowerings to honor someone other than a dead soldier than I want to bother with typing in here, but they happen a lot in these United States. A lot.
Governors of the several U.S. states or territories are authorized by federal law to order all U.S. and state flags in their jurisdiction flown at half-staff as a mark of respect for a state official or resident who has died.
This is about as straightforward and uncontroversial as it can get. The only controversy here is a manufactured one.