Word for nemesis that does not refer to a person

Solution 1:

Bane

noun

1. a person or thing that ruins or spoils:
   Gambling was the bane of his existence.

(Dictionary.com)

Your bane goes beyond just ruining you; it is your nemesis, it is always getting you and you fall victim to it very often.

Solution 2:

There's no reason you can't use nemesis. Merriam Webster's definition page gives several examples where the word "nemesis" doesn't refer to people:

On just the kind of putt that had been a career-long nemesis, he kept his head perfectly still and knocked the ball squarely in the hole. —Jaime Diaz, Sports Illustrated, 20 Feb. 1995 (from M-W)

Thus, once surgeons implant the new graft, tissue rejection—the unforgiving nemesis of most transplant attempts—occurs in only 3% to 5% of cases. —Christine Gorman et al., Time, 7 Dec. 1987 (from M-W)

Granted, these sentences all refer to the thing that is the nemesis, but this seems a natural thing to do in order not to keep the reader/listener hanging. Your example sentence, "Your greatest nemesis showed you your deepest fear," assumes that the reader/listener already has some idea what that nemesis is.

Solution 3:

You might use bête noire for this. In the context of your example it most often would be your greatest fear, but I think you could use it to say that the acknowledged bête noire showed you your actual, unacknowledged deepest fear. From Wiktionary:

Etymology
Borrowing from French bête noire ‎(literally “black beast”).

Noun
bête noire ‎(plural bêtes noires)

An anathema; someone or something which is particularly disliked or avoided; an object of aversion, the bane of one’s existence.

It is used for the kind of things you mention:

Several of the rules cautioned against Seneca's bête noire, anger. —Richard Brookhiser, Founding Father

But Ecstasy quickly became a class A drug and was soon seen as the bête noire of club life. —Mike Presdee, Cultural Criminology and the Carnival of Crime

For years, the public and scientists alike feared that lakes and forests in the eastern United States were being destroyed by acid rain . . . . Today, environmental issues are far different from those even 30 years ago. In part, that's because visible pollution has almost disappeared—the plumes from power plants are mostly steam (and carbon dioxide, today's bête noire, is invisible). —Richard L. Stroup, Eco-nomics: What Everyone Should Know about Economics and the Environment

I think it's especially useful for personifying/demonizing a more abstract concept (that doesn't actually care oone way or the other about you) as an adversary. So your example would read:

The relationship between you and your bête noire may seem to be purely an unmutual fight, but underneath the surface, your bête noire fuels you to greater heights.

(Wiktionary also suggests the similar bugbear.)

Solution 4:

You might consider kryptonite if the circumstances allow for it.

Oxford Dictionaries defines it as:

[mass noun] (in science fiction) an alien mineral with the property of depriving Superman of his powers

The book From Average to Awesome: Lessons for Living an Extraordinary Life By Jim Smith, Jr. uses it like this:

Bronwen, a close friend, recently told me about how her friend Denny summoned the courage to get rid of his kryptonite. She related how his sales job was causing him severe pain....