According to BBC Shakespeare Animated Tales-Julius Caesar, Brutus supposed to not kill Julius Caesar because it only makes Romans rebel especially Mark Antony. Brutus should think about the murdering deeply and do not follow on Cassius advice.
Julius Caesar is the most influence people in Rome, Brutus should know that. By killing Rome dictator, it only put himself in trouble. Even though Caesar was not a good person but he still loves Brutus. He provides the best education for Brutus and Brutus have to think wisely before make the decision to kill his adopted father.
Brutus should realize without Caesar he is nothing. By killing Caesar is not a noble motive but it is more to revenge because the idea derives from Cassius not him. Cassius seems like to hate on Caesar because he had all the title and respect from Romans even though he is a bad person.
Caesar is an old man and he would not protect himself if all the 12 persons attack him. The consequences of the murder also not been thought by Brutus, because of Cassius words he does not think the results on his action.
In conclusion, Brutus has no reason to kill his adopted father because Caesar is an old man. Brutus actually did not respect him as a father although Caesar had killed thousands of people but he still cares on Brutus.