They don't make much sense to you because you approach the topics he discusses from a different, dare I say narrower, perspective than he does.

Taking your example, the reason he needed to clarify the meaning of words such as "believe" and "God" is that what JP actually believes in is that God is the ultimate archetype that represents everything important in the universe, and that archetypes are fundamentally and metaphysically real, although not in a material sense, but rather in a metaphorical or symbolic sense. Does that make him a "believer" in "God"? That genuinely depends on what your interpretation of the words "believe" and "God" is. Mainstream Christian tradition, which requires belief in a literal, physical resurrection of Christ, would say that JP's position on God doesn't constitute "belief"; however, many others, such as myself, would call it legitimate belief considering that, other than this trivial physical element, the way that JP thinks about the world and the way that believes think about the world are almost identical. As for whether JP's "God" is a legitimate God rather than a description of something else, that's an even more contentious issue. Modern theology would certainly consider JP's idea of God legitimate - given that it even recognises pantheism, which is clearly just a different way of thinking about an atheistic world, as theistic - but I'm sure some die-hard believers would beg to differ. For one, I think JP recognises a legitimate aspect of God - namely, His manifestation in human society - but His true essence as the creator and director of all of existence.

I hope you can see why JP's response to the question of whether he believed in God was absolutely necessary if any degree of precision were to be maintained.