Certain parts of Watchtower doctrine appeal to logic--especially when compared to traditional Christianity. For example, Witnesses love to harp on the Trinity doctrine using arguments such as "who was Jesus praying to?" and "who resurrected Jesus?" and "Jesus said the Father is greater than I am," etc.
They use similar arguments to deconstruct other traditional teachings (Hell, immortal soul, etc.). If you buy those arguments, then you've just excluded almost all major Christian religions. Combine that with the appealing promise of living forever on a paradise earth, and I can totally understand how folks get sucked in.
Of course, there are plenty of Watchtower doctrines that are laughable (trumpet blasts of Revelation, 2300 days of Daniel, etc.); confusing and contrary to common sense ("generation," Jesus isn't your mediator); and slanderous of God (only JWs will survive the "imminent" battle of Armageddon).
But Witnesses don't emphasize these teachings or their history of false prophecy, which should be enough to convince a fair-minded person that the Watchtower is not "God's visible organization." Unfortunately, it takes a while for most to figure this out. By then you're often in so deep that it's tough to get out.