By: +David Herron; Date: July 8, 2018
During the 1st Doctor's era we did not even know about Gallifrey or Time Lords or any of the rest. He was an alien from Earth, who had stopped there for awhile, and was trying to gain control over the TARDIS.
By the end of the 2nd Doctor's era we learned about the Time Lords, and that The Doctor was something of a renegade.
But ... why ...?
With a reasonable facsimile of Bill doing the questioning, the First Doctor is asked not to explain why he left, but what he was running towards. That is an interesting take on the question, rather than the negative (why leave) viewpoint, it's the positive viewpoint (what did you hope to accomplish).
That drew an interesting answer.
The universe has "Good" and "Evil" and the question is, why does Good ever prevail? The Doctor explained that Good isn't exactly the best survival choice, and that committing Evil is often the better choice. What The Doctor wanted to learn is why does Good prevail.
This does a lot to explain why The Doctor takes the stances he often does. Rather than to seek out to destroy evil, he is often in the position of desiring to help supposed evil to do better.
How many times has The Doctor wanted to convince Daleks to be nice? The other half of this snippet showed "Rusty", a Dalek he managed to show Beauty to.
How many times has The Doctor wanted to reform The Master? He got a big opportunity in the episodes prior to this one, only to have it turn out badly.
These and other actions by The Doctor are what one does when one is exploring Goodness.