'Magical girls are evil!' inciting incident

So, I am trying to work out the personality and backstory of one of my characters, Alyssa, a Muggle woman who hunts down and kills magical girls for a living. But I am having some trouble with coming up with a believable reason for why she goes killing magical girls in the first place.

The main motivation I want her to have when going off hunting magical girls is that she wants to be in control of her life, or at the very least know everything so that she can be prepared for whatever situation she is facing. Magical girls, as they possess all kinds of magical powers, are a danger to herself and the ones she cares about, so she wants to eliminate them all and remove that danger.

Now, as to what triggered this, I was planning to have Alyssa be involved or witness an incident, during which she comes into contact with some magical girls, and realizes that her sister is one of them. This event is such that it completely messes up with Alyssa’s organized world, and maybe somewhat harmful to her friends and her under control life. In other words, it plants in her mind that magical girls are evil, and must be dealt with. Alyssa will then start researching who these girls are, and will subsequently discover things that will only reinforce her initial idea that the only option to deal with them is to kill them all.

So, what kind of incident could I use to show to Alyssa that magical girls are evil, and how could I reinforce that idea, without her realizing that there are ‘good’ and ‘bad’ magical girls and associates, and that she would be better off trying to help out the good ones?

One possibility is always to give these "Magical Girls" another code of morals than standard human beings. They aren't evil per se, but if judged according to normal standards their actions may be perceived as evil. Think a cat playing with a mouse - the cat doesn't consider its own actions as "evil", but a human looking at it would often find same actions cruel. Perhaps the magical girls are arrogant, and with a flick of their wrists they uprooted Alyssa's world without even thinking of it, because she was just another normal human being. Perhaps it's part of some strange Code that the family of a Magical Girl must be deleted/their memories removed, to conserve the secret of the Magical Girls (if it is indeed a secret). Perhaps Alyssa and her family/friends were just in the wrong place at the wrong time, and became "collateral damage" to the Magical Girls.

There are really several possibilities, it's just about settling on one.

Put in a bit of grey. Have the bad magical girls keep their less-marketable habits in secret, while the Good one either don't think though the consequences of all their actions, or do questionable stuff to maintain order ("Magical-girl brutality”, for example, or the aftermentioned memory wiping".) while who's good and who's bad should be overall obvious, it should only be so to those with the nigh-omniscient perspective that comes with being behind the fourth wall.

To be honest, what has already been said seems good. Have our commiter-of-hate—crimes having an immense requirement for order in her life would help, as well as having her would view irreparably changed by the relation of magic and the like.

Do you want her to have a point or not?

If you want her to be at least a little sympathetic, you should have her bring up the fact that where magical girls are, villains will follow, leaving property damage and injured people in their wake.

With superheroes this can be a pretty stupid argument (yeah, it's totally Spidey's fault that bank robbers are dicks), but with mahou shoujo it can hold some serious water; between the local Dark Magical Girl with a fixation and the Dragon out to snatch the Pure Love Helm, your standard-issue Sailor Whatsherface attracts a lot more bad folk than your average Japanese city would normally see.

Also, consider what the source of the magical powers the girls have might be; do their transformation hair-ties run on the energy put out by the soul trapped inside?

Also also, maybe their methods are inhumane, because the monsters of the week are possessed people, but they always kill them rather than healing them?

You could have her beef be about what they do to uphold The Masquerade. Maybe someone she cares about was Killed to Uphold the Masquerade.

Or, whoever the magical girls are fighting, maybe she decides the magical girls are being unfair to them. Making a hero's targets sympathetic is often a good way to paint the hero black.