Some would say it began a long time ago, eons even. Others would say once upon a time and then there were people, who kept trying to convince you that it just started somewhere. Even if that when is relative and essentially does not matter because who is so much more important anyway. Sometimes the why too but that just in rare exceptions that nobody cares about.
In our specific case the why is a tad more important than the usual not at all. You cannot just claim that old wise men just take a hike over impossibly tall mountains following intricately winding paths because of their own crankiness. Not that other old whack jobs missing the wisdom would not be able to do just that, most of those have professional reasons for doing so in the first place. Our old timer is not just old but wise too. And is following an inner calling¹ that hundreds before him have and theoretically hundreds after him will. He was on the journey to find his successor.
Now one might wonder why he would wait until he was too old to hold a sword properly to do so? Heroes are usually young valiants that save princesses and smite dragons². Now you should realize why. Not only heroes need successors, the wise men that are usually called mentor do too. Imagine that, even those don't pop out of thin air knowing about the universe and stuff.
Back to our wanderer. He is as mentioned a mentor and did help one hero or another with fulfilling his destiny and sometimes with a little push³. Still even mentors age and at one point there has to be someone to take up the mantle and follow in his footsteps. Though in this case…
Nobody in their right4 mind would be wanting to follow the footsteps of an old geezer, that slips on a snowy, narrow mountain path, screaming "Bloody ice!" while falling. The sword he carried ripped away and as coincidence will have it, ricocheted off the harsh mountain ridge with a clear pling and plummeted to depth beside the steep slope. It was supposed to be the first example of his future disciple's work, the weapon of the first hero he would be helping on his path. On the other hand are old cranky codgers not supposed to climb narrow paths in the highest mountains in deepest winter which already the young folk staves off of in summer.
--------------------------
¹Not to confuse with the inner voice and only existing in single number and tone.
²Depending on the species it might just be the other way around. You won't really catch the interest of a young wyvern with the hand of the princess except you offer it with the rest of her as a snack.
³Sometimes quite literally with a very adamant push of a boot.
4Most people outside their right mind wouldn't want that either.