What is it that makes people develop and hold onto anger when they haven't been harmed in anyway?

Anger can proceed from jealousy, resentment, impatience, frustration, or any perceived threat to our well-being.  Does not just come from being harmed and many who are harmed do not react with or in anger. 

Anger is part of the defense emotion that mammals possess. 

Some people look for things about which to be angry because that's their nature. 

probably nnental issues

Because some things are just plain philosophically abhorrent to people with the appropriate insight into what is happening.

anyway any way

They can hurt your feeling or tread on your toes figurreitly speaking...both don't actually  hurt ,but both can and do actually  leave a mark that impossible to erase.....:( 

Empathy, conscience, morals.

Harm and anger are not joined at the hip, Weylon. It is perfectly normal to feel anger toward a particularly dire event that you play no role in. 

Example:
3,000 people died in the WTC on 9/11. I wasn’t one of them, I wasn’t harmed, nor was anyone I knew. Probably most on here weren’t either. But there was plenty of anger all around. For obvious reasons. Unjustified? 

Lots of reasons.
And it depends what you call harm.

The more someone is identified with their ego, the more they will feel hurt by insults and slights.

Some people are highly "other centred", meaning that they are insecure in their self-esteem and therefore highly dependent on the good opinion of others in order to feel good about themselves. These people will feel especially wounded by slurs.

If they perceive the one who hurt them as holding a fixed negative judgement, they will assume that it is an indication of dislike or hatred and be likely to stay away.

Sometimes a negative judgement might be unfair or unjustified - but the person gets no chance to present the facts.
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Don Barzini makes an excellent point; out of empathy for others, many of us may feel anger at the mistreatment or harm done to others.
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Some people are locked into anger personalities. Anger can be an addiction, creating the temporary illusion of energy, power and righteousness. Anger can be a means of attempting to manipulate and control others. Anger can also be a side effect of speed or ice addiction.
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Many people become angry due to fear; they perceive a possible harm being threatened.
Anger can be one of the drivers for defending boundaries.

  This is about those bad tildes you sold me back in 2014, isn't it, Weylon? You think I should just forget about it, just let bygones be bygones, I suppose that's your game. Grrrrrrrrr.