Especially in certain places where there aren’t any descent roads or no roads at all. Depending on the motorcycle and the riding skills you have, you can go to places that are hard to reach. My bike was the best companion on my way off-the-beaten-tracks adventures in mountainous Turkey, in Northern Thailand’s hilltribes, or on Bromo’s volcanic sand dunes in Java. Also, it keeps you independent. You make your own schedule and draw your own way.
One time, when we were riding in the jungles of Indonesia with my partner, we were not able to find a hotel before the heavy rain started and it got dark. We ended up riding 14 hours, half of it through big muddy puddles under the rain until we found a place to stay. It was one of those days when I had to go way beyond my physical and psychological limits. If you like being challenged in this way, adventure motorcycling can absolutely offer you what you are looking for.
Each day is fresh, each day is brand new. Packing and heading off to the new horizons everyday without knowing what the road will bring is one way of keeping you outside of your comfort zones where life gets interesting. For instance, while planning to reach a certain destination at a certain time, you might end up having a mechanical/electrical problem or flat tire in a remote area, you might find out the path you want to follow is closed or the weather conditions prevent you from continuing at the speed you want. Instead of losing your temper, you learn to accept unexpected situations and act in the best way possible within the circumstances you’re surrounded.
When you ride, you always have to be present and alert. You should respond according the road and what comes in front of you. I remember, how much I had to be focused and responsive, especially riding in the big cities with dense traffic, unexpected driver behaviour, and off-road riding. It can get quite demanding but it also improves attentiveness to the present moment. 
Featured image by @eparrillaphotos.