Do guys think in depth like girls do, but pull the dumb card, so we don't expect much from them?
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Some guys are deep thinkers like some girls are, and some (like some girls) have the collective knowledge of a sack of hammers.
And like girls, sometimes, if it's convenient, some guys might play dumb, even if they were the 'deep thinking type'.
It's not uncommon either, though in context: a guy will have certain topics he's the 'master' of, and other topics he doesn't care about. Or situations: if a guy's not emotionally very empathetic, then he probably doesn't deep-down care that much about your Aunt Matilda's gout in her toe, and so he's probably going to genuinely forget about it (meaning he's not 'playing' dumb, but plain old forgot about you telling him). But if he's got his arms around you, and he truly screwed up big time, like a deer in headlights, he may panic and 'play dumb' to avoid a tiff and losing the romantic moment.
I've also seen both intelligent and stupid guys that were insecure do the exact opposite and make crap up from thin air, to either seem superior to someone else, or simply protect a perceived 'hole' in the domain for which they profess to be experts.
But in a nutshell, I would say this is an area where men and women aren't really all that different, even though the entertainment media portrays women doing this a fair bit.1