We don't kill any starlings or house sparrows. We've got a big backyard with lots of different birds. I suppose, most birds were invasive at one time. There's really not much you can do about birds flying into your area.
By invasive, he means that they are introduced, non-native species. house sparrows and starlings can throw the natural ecosystem out of balance by predating on other less aggressive native species, they will actually take entire area's over in competition, which is why they are two of the very few species you can remove at any time. North America went for (0) house sparrows in 1850, to 150 million today. The only species shown to have been able to compete with them is the house finch.