That's how great arguments work: you agree with every step (and after a while you start believing things you didn't originally).

And to avoid people giving in to their motivated cognition, you present the steps in order, and the conclusion at the end. To paraphrase Yudkowsky's explanation of Bayes Theorem:

By this point, conclusion may seem blatantly obvious or even tautological, rather than exciting and new. If so, this argument has entirely succeeded in its purpose.

This method of presenting great arguments is probably the most important thing I learned from philosophy, incidentally.