I'm looking for a metaphor or analogy for
experiencing more and more difficulties (after getting more familiar with a certain teaching or art). I think I have seen a few in the past but I can't think of them right now.
It sounds like you have opened a can of worms.
For every head you cut off, another two will grow back (Referencing the Hydra myth)
Related to the above, less violent:
For each question you answer/problem you solve, two more come/pop up.
A well-known saying refers to the situation where beginners think something is easy, but those at an intermediate stage are overwhelmed. It's often said as:
The more you learn, the less you know.
The more you know, the more you know you don't know.
Both versions allude to the discovery of an insurmountable amount left to learn.
One relevant expression is
One step forward, two steps back
although it implies that any small progress made is counterproductive, and you are moving backwards.
As suggested in the comment on this answer by Rikon, a more accurate expressiong might be
Two steps forward, one step back.
There's "snowballing". Once the snowball gets rolling it gets larger and larger.