The Watchtower twists the Apostles response to Jesus from "Whom else would we go" to "Where else." This changes the meaning from being a follower of Jesus to changing religions.
Getting to the question "Why not atheistic/philosophical scientific naturalism" I have found some things in my studies.
As a born in Jehovah's Witness I remember studying the Live Forever book with my dad prior to baptism. One of the things the Watchtower was still doing at this time was attacking other religions and beliefs. That is to say, the Watchtower publications didn't just show their reasons for why they think they are correct, but also deconstructed other faiths in regards to reasons they are "false". A problem I would find out later in life is that the Watchtower notoriously misquotes, takes quotes out of context, and generally provides misinformation/inaccurate information about other belief systems.
Another thing I found is that, because of the above, I found that ex-Witness tend to become atheistic as a result of this. Since the Watchtower seemed to do such a good job disproving all other religions and now that a Witness comes to find out the Watchtower is also false, the next natural step is become an atheist. I know I did, but I changed as I grew in knowledge.
I have studied human brain function and psychology. One noticeable thing is that the human brain is geared for religion. Even atheism tends to be religious. Consider the idea that "there is no supernatural". Really? How do we know. Rather, the claim is made by persons who believe that there is a scientific and perfectly rational answer for everything. That is to say, "I have faith that one day there will be a perfectly ration and scientific answer for the unexplained." Faith is the cornerstone of religion.
I am not saying there is a god nor do I believe the Bible is the answer. I have found that there are religions that seemed to line up with what science is now just discovering about the human mind and the universe. I recommend having a beginners mind set - I know nothing. True faith is letting go of belief and accepting truth as it manifests.