People/Politicians etc. have a long memory. If you think of it as a "treat others how you would like to be treated," eventually it will come down to a situation where Italy or some other EU nation will need assistance. In a "my people first" scenario, it's always easy to find a reason why you should not help someone else while justifying that your aid is needed by your people. By blocking the vaccine, they are setting themselves up to be retaliated against sometime in the future.