A lot of things can go wrong. As your setting the net for netfishing your arm or foot w/e can become tangled into it, and you can be dragged under sea.
You're setting the line for linefishing which has 500-600 hooks per stamp, and you need to stay close to make sure everything goes smoothly, hook each stamp together, and switch them as they go empty. A lot of the times they get tangled, and it stops moving out and then you need to cut a few angles and then suddenly it just bursts out. A lot of the times people get in penetrated through their hand, nose, a few have gotten it into their eyes. One guy I know got his pointy finger skins drawn off.
When killing the fish it needs to go quick so sometimes you might end up cutting yourself or even stabbing yourself. I ended up stabbing myself into my hand so I had to take a sickleave for two weeks.
A lot of the dangers occurs when fishing alone where people accidentally fell off board, and there is no one to know what happened. A guy fell off his boat in March, and died. People didn't know he was missing until like five or six hours after he fell off his boat.
There might be a fire on the boat that you cant stop so your ship goes down. Your ship starts taking in water. Boats have lifesuits, and lifeboats. These things can often go wrong. Keep in mind that my county has a total population of 70k people, with a greater land area than Denmark. Thus the general fishing area is pretty vast. The seaking helicopter base is quite far away, and people I knew almost died out on the Barentsea last year. Article regarding that incident;
http://www.vg.no/spesial/2015/ostbanken/.
Not saying that people are dying everyday, but fishing is the deadliest job based on statistics. There are a lot of safeguards in place to prevent it. There are frequent accidents, and I think there is around 1-2 deaths related to fishing per month.