Why Dany did it
Anyone who feels Dany's reaction wasn't justified or easily understood has never been an underestimated women, painfully dealing with having to over perform to be recognized. Just moments before Dany's decision, we heard Cersei state "we just need one good shot". After everything Dany did, Cersei (as a proxy for many in westros) saw Dany as a meaningless girl that happened to have a dragon. Obviously Dany couldn't hear Cersei but it's not a stretch to believe that she realized people were still thinking that. All Dany ever wanted was to be taken seriously but time and time again she had to prove herself .and so she did...again.