If a tree has been stricken by disease or insect infestation, it may become a hazard. The structure becomes weak, which could cause the tree to fall. It has probably already lost large branches due to weather and could possibly be completely dead. The last thing you want is for a wind, snow, or ice to knock the tree over. This can damage property and can severely injure or even kill people and animals.
Trees may also be a hazard if they have been allowed to grow into power lines. Trees that hit utility lines can injure people, start fires, or cause power outages. Even if a line is down, it can continue to conduct electricity and that is something that can create a very dangerous scenario.