Dogma is almost entirely built out of logic. It may not be logic that YOU agree with, but that doesn't mean that dogmatic principles aren't built out of logical chains from previously accepted premises.
Granted, in its most extreme form, you get stuff like the "witches weigh the same as ducks" scene in Monty Python and the Holy Grail (which is a pretty good example of how logical deduction works in general), but that's still logic. Even if it's faulty logic.
The real trick to dogma is that once logic determines what dogma IS, followers are discouraged from attempting to use their own logic or newer premises to revise the existing dogma. But even then, dogma can change over time (the Catholic Church of today is very different from the Catholic Church of 1920 in a lot of ways - there've been a lot of reformist Popes over the last century or so).
But if you really hate the entire concept of dogma, you can always go Discordian and follow catma instead.
