The way I see it, Anders was a coward.
Elthina was the one who would have broken the stalemate between Meredith and Orsino one way or the other. Consider things from her point of view. One the one hand, she has Meredith who represents the military might of the Chantry currently in Kirkwall, and on the other, she has mages who are in the keeping of the Chantry through the Circle. She has to know that conditions for the mages are horrible, but she does nothing about it why?
Well, what if she knew that Meredith was losing it? And what if she knew that Orsino was not as clean as he made out to be and that Kirkwall did have a problem with blood mages in its ranks. How do you choose between those options? Any choice comes with some bad implications, and if you side against Meredith, she might snap and turn on you with her army and annul the mages anyway. So, Elthina waits and hopes that something will help her decide or change circumstances or that she can stand between the mages and Templars in the meantime.
But Anders can't take the chance that Elthina will take a side, and worse that she will side against mages. So he acts pre-emptively before anyone really knows what Elthina might have done. He's a coward and takes the easiest and most drastic way to force the choice he wants to impose on everyone else.