Final answer:
Gaius Gracchus wanted to grant citizenship to all Italians to create a more inclusive Italian Republic and strengthen the Republic. The Senate resisted, fearing that this would erode their power and threaten Roman societal institutions.
Step-by-step explanation:
Gaius Gracchus desired to extend full citizenship to all of Rome's Italian subjects. He saw this as a way to transform the Roman Republic into a more inclusive Italian Republic, believing it would benefit the Republic as a whole through, for example, a broadened base of military recruits. The opposition from the Senate was rooted in the belief that extending citizenship would dilute the power and prestige of the existing senatorial class, overcrowd the Senate with new members from wealthy classes of former enemies, and threaten the traditional Roman social hierarchies. The Senate also feared the loss of their large landholdings and the disrupting effects on the Roman military and economic systems.
Indeed, such extensions of citizenship would have potentially upset the stability of the Roman state institutions and society. By the time of Gaius Gracchus, Roman citizenship was still a valued and sometimes jealously guarded status. The suggestion to extend citizenship broadly was perceived as a threat to the established order and power structures, explaining the strong resistance by the Senate.