The BBC reports that the European Commission has told Italy to revise its budget, saying that the draft presents particularly serious non-compliance with Eurozone rules. Yet the maximum permitted deficit is 3% and the Italian government states that its budget has a deficit of 2.4%. If the Italian budget deficit is less than the maximum permitted 3%, on what grounds is the European Commission telling Italy it must revise its budget?
Italy is not just planning a high budget deficit, it has a very high level of national debt. (As of 2017, it was 131.8% of their GDP, second only to Greece) This makes their deficit riskier than it would be for a country with a lower level of overall debt. Italian banks also own a lot of that debt, and there is a fear that government intervention in the banks (which has already been taking place) could lead to a vicious cycle, collapsing both.
It is worth noting that the Italian government running a substantial deficit is a fairly new phenomenon - they were able to calm investors until recently by running a budget surplus.
It appears the problem isn't the deficit (the loss from an individual budget) but the size of the existing debt itself. From a report in the Guardian
Italy’s public debt is worth more than 130% of the country’s GDP, the second-highest level in the EU after Greece and more than double the bloc’s limit of 60%.
In effect, the EU don't believe that the budget the coalition have announced represents a serious attempt to control their spending, or to honour previous promises made when receiving EU financial support.
As mentioned in previous answers, it is not just about the deficit but also about the already high level of national debt.
Furthermore, the Italian government was initially expected to aim for a 0.8% deficit in 2019 before announcing last July that they would not be able to hold that.
So instead of reducing its deficit as expected, the Italian government is expanding it by quite a bit. And while some expansion can be tolerated, this one poses a lot of problem because of its structural nature. Indeed, some of the reforms that the Italian government wants to carry out (and so included in their 2019 deficit/budget), such as a basic income, lower retirement age and lower taxes are structural in the sense that they will have long term effects on spending and so on the government's deficit. This is contrary to what the European Commission is trying to achieve: healthier budgets/finances
Italy doesn't infringe on its obligation to keep its deficit below 3 %, but on its obligation to keep its debt-to-GDP ratio below 60 %. Most countries in the European Monetary Union (EMU) have an excessively high debt level after the economic crisis of 2007, but all countries seem to be engaged at stopping the debt from spiraling out of control.
Italy is the outlier. It openly defies the rules of the EMU. The Italian government doesn't seem to be serious about stabilising or even lowering its extremely high debt-to-GDP ratio (about 130 %). The government wants to simultaneously increase its social spending and lower its taxes. Higher spending and lesser income doesn't lower one's deficit. Sure, the Italian government predicts that its reforms would unleash economic growth, but neither the markets nor the non-Italian EU politicians believe in these predictions.
It's not only about Italy being a bad example. (Others have been, too.) The Italian budget directly threatens the economic stability of Italy and the survival of the EMU. If a country with a lower debt-to-GDP ratio (e.g., Estonia, Bulgaria, even Germany) did so, nobody would be seriously concerned - but in the case of Italy a default seems imaginable. And Italy is not one of the smaller member states! The European Central Bank is already owning a huge pile of Italian government bonds and would be obliged to continue buying them in large quantity. The markets don't want them as shown by the large spread. (= risk premium, the difference in interest between Italian and German government bonds, which are considered almost risk-free) The ECB-owned bonds would lose much of their value. Furthermore, the citizens of the other Euro countries would be on the hook for an Italian banking crisis.
Rich countries are interested in low inflation because inflation reduces the general worth of money and therefore penalises those who were wealthy enough to save and lend their money to others. Poorer countries with debt on the other hand are interested in moderate inflation because the reduction of the worth of money means the reduction of the value of their debts. Currently there is low inflation despite the steps taken to expand the euro in circulation through quantitative easing. In anticipation of rises in inflation it appears the ECB/eurozone (i.e.: Germany) is pushing for lower deficits. If quantitative easing stops (as is planned for the end of this year) countries with high deficits (and high debts) will have trouble financing themselves. At that point there will be a crisis, and the solution would either be to reinstate quantitative easing which the rich countries in the eurozone do not want, or the country would have to leave the eurozone. While the leaving of Greece from the eurozone would have perhaps a small impact, Italy on the other hand is a large country which can have a much larger effect on the eurozone.