Lowering of the flag is a gesture of loss. While the history of this gesture can be unclear sometimes it represents loss and should not be perceived as a sign of division. It can conjure up images of sorry and death but should be seen as a sign of respect and appreciation to the loss.
Mostly when we see a flag at half-staff, we assume there's been a death or several, and that's a pretty universal assumption. It's another story, if for example the flag at half mast is a Confederate flag, or the flag of a hate group or country that has invaded another.
While lowering a flag to half staff might have meant blood in the past, today it is a sign of mourning. A person has to have had a wonderful story and contributed in society in order to have flags lowered to half staff for her. It is a sign of respect and memory to a great person.
Flying the flag at half staff is a symbol of death and a way to honor those who have lost their lives. It is not and never will be a sign of division. Although there are some people who would like to change the meaning of flying a flag at half staff, it will always be a show of respect for the deceased.