When Terry McGinnis found himself on the grounds of Wayne manor after being chased by Joker thugs. He's assisted by old man Bruce Wayne who decides to take him in as an assistant. After his father is killed and he discovers that Bruce Wayne used to be Batman he asks him if he can take up the mantle so he can avenge his father. When Bruce refuses to let Terry take revenge he decides to steal the batsuit and take matters into his own hands. After their initial conflict Bruce and Terry decide to work together and Terry becomes the new Batman.
Terry would make a good president because he's determined and respects history without being unreasonably devoted to it. As Batman he proved that he could take an old tradition and adjust it ot fit the needs of a new era. He also has proben that he can come up with creative solutions to big problems. An example would be when he decided the best way to defeat the resurrected Joker was to make fun of him which is something that had never been tried before. All these elements of Terry's character would make him a successful candidate for president. Wikipedia.
Batman Beyond's campaign platform includes rehabilitation, measures against global warming, and programs for troubled kids. One of Batman's key principles is to not kill this means that Batman Beond will be focused on rehabilitaitng criminals instead of locking them away forever or executing them. Batman Beyond being from the future is very worried about problems that will have long term impacts whih is why he's focused on reducing the negative impacts of climate change. Since Batman Beyond grew up as a troubled kid he'll create new programs that will help troubled kids find their way through internship programs and job training. Overall, Batman Beyond's platform is focused on fixing the future by reducing crime and helping troubled kids.