There are several ways in which to answer this question. Let me offer a few points.
First, all through the work, Shakespeare is pretty clear that Caesar was ambitious. This is clearly seen in Caesar's actions, as he seeks to gain complete control over Rome. This is no small point, because from a historical perspective, many Roman writers stated very clearly the evils of ambition. For example, Sallust, a Roman historian makes this point repeatedly. In fact, according to Sallust the fall of Roman society can be attributed to ambition.
Second, Caesar took on the title of dictator for life. This, too, was no small action. Dictators in Roman society were only for times of emergency. So, when Caesar took this title for life, it did not settle with many people. Moreover, Shakespeare intimates that Caesar was aiming for the crown. This would have made him into a king, the very thing the Roman hated the most. The very fact that there was this suspicion suggest that Caesar was too ambitious.
Third, the very fact that Shakespeare portrays Brutus as the most honorable Roman says a lot. In other words, if an honorable Roman was apart of the assassination plot, then Caesar must have been reaching too far in his ambition. This might be the strongest point that Shakespeare makes.