Yes, we spend a lot of time traveling to and from different countries, so it is convenient for our family's lifestyle and so far has worked well. I have nothing against public education and support it, but for our family at this time, it works for us. We have no problems immersing our children in either culture since my wife is from Argentina and I from Texas myself (they spend substantial time with our families wherever we are), so we have stuck with this for now. The nice part about living in Argentina is that there are so many social clubs and cheap activities that can be paid where children can do activities with other children, and get involved socially. Our family is able to do it and we are seeing benefits. If you want to do it but are afraid of teaching, there are also online programs that are pretty amazing.
Although my reasons for homeschooling children are not religious, is there a problem with homeschooling your children for religious reasons? I thought we lived in Western democracies, where freedom of religion is protected.