Why should I show emotions rather than telling them?
Which do you think would engage a reader more:
He was very agitated.
He paced back and forth, running his fingers through his hair until it stood on end as if he'd been electrocuted.
The second sentence allows the reader to form a mental picture, while the first one merely tell the reader how someone felt. As readers, we want to "see" in our mind's eye someone as they're behaving or emoting on the page.
It's more difficult to show your readers the emotions your characters are feeling, but it brings the reader into the story instead of keeping them outside and observing.
Use your own emotional responses to create life-like behaviors in your characters. Not everyone paces when they're agitated. Have your character chew on her fingernails or binge-eat to try to relieve her agitation.