The trick that works most of the time is the security issue, a little googling and evidence shows itself in blog posts all around the web.
I rarely have tech wise clients, though some of the few who actually DO know a bit about web technology and are on the Wordpress hype train, I take out this weapon:
"Did you know Wordpress in in fact a blogging software?? Then, let's think again, do you think your website is a blog?" It's like using confusion on a Pokemon. The train of thought is that they are using the wrong tool for their problem and that actually stops people to think, what do I want from my website??. I then go with the "more professional, custom solution called Processwire" pitch. Also, very important, I talk about how costly can Wordpress become if you want to start customizing content management and display, unsafe plugins, and the safe ones that mean extra costs, maintenance for Wordpress updates, etc. With PW, you get what you need, solid cost effective solution.
Though, the smarter ones will say: Hey, everyone is using it!! What's the deal with you weirdo!! After that, I'm left with my last weapon which is walk away!! And impressively, that one actually sometimes work! It's like, after showing them that the way to Wordpress goes through Mordor, they start feeling the fear and come back.
ps. I'm really liking the LOTR metaphors.