My deal-breaker is STUPIDITY. I can absolutely not stand a horse who is truly, deeply, intractably STUPID. Lots of "difficult" temperaments can be worked with, lots of training issues can be reprogrammed, and a horse who's smart enough to be self-protective will usually look out for you by default when you're sitting on his back.
But the kind who can't find their own FEED bucket in the field--after 3 YEARS? No, thanks! :lol: