The problem is not having a negative emotional thought, but obsessing over it and letting it overpower the other thoughts you have.
Most of the time the negative thoughts are just imaginations, histories that our mind creates and makes real. For example; it's late at night, your daughter or girlfriend hasn't returned home yet and their phone is off. You start to imagine the worst scenarios (accident, rape, cheating, whatever..) and your mind is stupid enough that it starts to believe them and making those scenarios real. You start to get worried, then anxious, then angry at them for not thinking of you and how worried you are. Maybe you are really angry when they get home and scream at them just to discover that they have been somewhere safe all night and just ran out of battery.
Being able to realize that those scenarios are just creations of your mind and snapping out of the obsessive loop of thoughts it's one of the most important things you can learn in life.