I didn't say anything about religions and ideologies not using reasoning. Anyone who has read, say, Thomas Aquinas is perfectly aware that religious people can use all kinds of complicated reasoning to justify their beliefs.
What I did say is that the set of beliefs in question are "all asserted as justification for each other in what amounts to a logical circle". For example, Thomas Aquinas spent a lot of time building up a huge edifice of interlocking propositions about God, all logically related to each other--but they don't connect to anything else. They're just a free-standing, self-consistent logical structure that can't be justified in any way except by claiming that it justifies itself. It's not that Aquinas didn't use reasoning; as noted above, he did--lots of it.