I have a couple of friends who believe that riding a road bike--regardless of handlebar setup, size, fit, etc.--is much more difficult than riding an MTB/ATB (i.e., mountain bike), because it is harder to balance. Maybe I've just been riding bikes too long, but... no?
Body position makes a big difference in balancing (e.g., the muscle habits to balance in a bent-over "racer" position are different from a more upright position), and skinny/hard road tires can cause difficulties with irregularities in the road surface. Bike geometry and fit matter, as well, though both of these friends ride MTBs with geometry not totally dissimilar to road bikes and which put them in a very similar body position. The wheel sizes aren't wildly different, either.
Balancing itself--the issue these friends are convinced is the problem--doesn't seem to be about the tire size; it's about steering (with some baseline velocity). Am I confused about this? I'm not an Excellent Cyclist (i.e., I've never done trials riding or racing), but I've been cycling here and there for a few decades. Maybe I've just adjusted or something? I get on a road bike and it's pretty much the same balancing difficulty as a mountain bike. Am I wrong about this? Are my perceptions altered from all the years of casual bike use?