We know from Pottermore that Dolores Umbridge has a very short wand:
Wand: Birch and dragon heartstring, eight inches long
Also, that short wands tend to choose wizards with something lacking in their character/personality.
Most wands will be in the range of between nine and fourteen inches. While I have sold extremely short wands (eight inches and under) and very long wands (over fifteen inches), these are exceptionally rare. In the latter case, a physical peculiarity demanded the excessive wand length. However, abnormally short wands usually select those in whose character something is lacking, rather than because they are physically undersized (many small witches and wizards are chosen by longer wands). - Garrick Ollivander, wandmaker
We know for sure that two things Umbridge lacks is empathy (she is really sadistic) and good taste (here I'm translating from German, I hope it means what it is supposed to mean!).
Now my speculation: because of her narrow world view and because of the way she seeks and uses power, I had the impression that she must also be lacking self-esteem and/or self-confidence. It's common that people become narrow-minded and power-seeking (not necessarily to the extent Umbridge does) among others because of that.
Is there any more information on this issue?
Edit: as Hellothere_1 pointed out, bullies have actually high self esteem. Hovewer some people with low self-esteem might become among others arrogant, so I guess I somehow mixed both 'traits'.