Yes, they can be dangerous! Bulls or in as on our ranch Black Angus bulls. These are some of our bulls. This bunch ranges in age from one year to three years old. They weigh between 1300-2100 pounds. Currently they are about a month and a half away from being turned out with the cows. They will spend about 45 days or so getting the cows bred. Then they go back to just hanging out in the bull pasture.
Most of the time they are pretty docile and even friendly. Most of them will eat out of my hand. Three of them love to have their heads scratched. One of the top three traits we chose our bulls for is temperament. We have bloodlines we have found to be great for that in the bulls and they pass it on to their offspring. If one of our bulls is aggressive, he "goes down the road" to the sale barn. We don't need one that we need to be afraid of.
However, as friendly as they can be, they also can be moody and testy. Especially when they think it is time to get turned out with the cows. Even the ones who are friendly are less so when they are wanting to get to the cows and when they are out there with them.
One thing to keep in mind is, the bulls have their pecking order. As people, we are at the bottom of the social ladder, no matter how much a bull likes us or seems tame and friendly. They spar back and forth reminding each other just who is ranked where. All it takes is a second for a bull to think he needs to remind you of just how low are are and he can hurt or kill you. He might not mean to really hurt you if he pushed you but he doesn't realize how much he can hurt you.
When they are sparring back and forth, the best place to be is no where near them. They are oblivious to everything and everyone but the one they are fighting with. Imagine getting between to bulls each weighing a ton!