Brain activity is a SUFFICIENT condition for life, but not a NECESSARY one. The very young human embryo is not complex enough to need a brain. But when he does, by virtue of his ability to grow and develop (something that clearly shows he is alive), he will simply grow one.
Also, what does the brain do? when our brain dies, it ceases to keep the parts of the body working together- we lose our "organic unity". Very young embryos, although they do not have a brain, are still organically unified and thus very much alive.
Again, you have no argument.