It commonly seen it apocalyptic fiction that if the government can't save a section of the populous they simply kill them an example would be the beginning of Last of Us. Assuming that the zombie apocalypse happened, why would a government kill civilians instead of ignoring them or letting them die?
If you're dealing with zombies then the principles of forest fire fighting apply. To put a break between what you can save and the incoming danger you need to create a gap with no fuel for the fire. You either remove or backburn the fuel.
In this case the fuel is people.
In a zombie apocalypse anyone who is killed by a zombie becomes a zombie, so that might be a pretty good reason.
After all, every victim becomes another enemy throwing itself at you.
I would, however, like to point out the downside to this approach: it's entirely possible that once you're known to sacrifice civilian lives for "the greater good* " you will lose a lot of trust, and may even have people turn against you.
For example, if a massive zombie hoard is besieging a small town, and you nuke it, thus destroying millions of zombies, and allowing the military to go on the offensive you're a hero.
If, however, outbreaks start in NY, and no one really knows how bad it is, but you nuke it (even if your reasons are solid) people will question your actions. Were there really that many infected? Were there really no survivors left? Was the situation truly that hopeless?
*(bonus points if you had that one scene from Hot Fuzz pop into your minds when you read this)
There are several reasons other than the obvious "If we let them live they could become zombies too"
Collateral Damage. Zombie outbreak in LA. Nuke California to save the world. (don't do it. It would ruin the perfect weather)
Lack of Resources. Limited food, water, weapons, living space, etc... "We can't save you all. Those who we don't save we have to kill."
Government Corruption. Those people have always been very rebellious. Nuke them and say it's for the greater good.
Fight for resources
The firebreak/don't let the zombies grow in number looks like a nice option; but you could say that if you give some sort of weapons (even melee weapons) to the stranded survivors they will probably kill more than their numbers of zombies.
The reality is that such a reason is just a white-wash (it is said this way?) of the real reason.
You do not want the risk of (too many) people surviving the zombie apocalypse.
After the zombie apocalypse is over, most of the productive resources of the world will be in tatters. You may still have arable land, and with some luck some seeds1, but you will have no fertilizers, no insecticides, little fuel for harvesters and other machines...
If you have a small population used to be quite organized, you might make it work somehow. But if in your area there are hundreds of thousands or even millions of disorganized, roaming survivors looking for food, the outlook is bad. Worse even that when you were fighting zombies, because you were able to outsmart the zombies and the zombies cannot shot back at you.
Of course, telling your people that you plan to massacre such a great number of their friends, relatives, neighbors2 just to ensure their own survival is likely to generate conflict, demoralization, and even internal fights. And when all of this is over, even if they agreed with it, you know they will point at you as the responsable of all it.
So, you tell them that black lie that the killing is to avoid the production of more zombies, even if your people know it is a lie they will abide to it because it will be far easier than accepting the truth.
1 Again, if you are lucky. Nowadays almost no farmer stores seeds for the next crop, they are bought to private companies. If your area is too far from one of the distribution centers then well, no seeds for you.
2 Ok, maybe some people won't miss their neighbours much.