To get to the other side.
I do get questions on donkey behavior (yes, including this one). I think it is safe to say that donkeys just go where their little donkey brains send them.
Browsing is a donkey characteristic: they are not always eating. (They have slow metabolisms.) They do remember where they found what they liked, and will return to it. They do follow their own trails. But they also just mosey around. Going downhill is easier than going uphill, 'eh?
Why do they just stop and stand in the middle of the road? Well a donkey spends a large part of each day standing and it has to do it somewhere.
What a donkey does, when posed with an unknown and possible threat, is stand and assess. They can do this for a long time. They will look you head-on in the road, in your driveway, in your back yard, anywhere. They are just going to stare you down.
Let them. The choice you are asking the donkey to make is, "Do I mosey on, or do I charge and kick." The donkey will make this decision, not you. Why press your luck?