I do not think that it's just the government.
Many Italians find that there is too much immigration since years.
And 50 000 young Italians leave the country each year to try their luck elsewhere, and that Italy becomes a country of old people, I saw on the TV.
They said that Italy is losing its youth because the economy is bad and there is no work for young Italians.
A strange paradox to welcome the youth of the other countries when there is almost no of work for the youth of the country which welcomed a lot until now.
It seems that there is an awareness of the Italian people to take care in priority, of his youth, of his children.
Different children and the answer to your riddle. Italian youth are leaving because there's no 'middle-class' work. Opportunities for career advancement are seriously limited because of cronyism and nepotism at a wide level (especially here in the south where most of the emigration is coming from).
Meanwhile Italy has a lot of low-paid, unskilled work on offer. Whether it's on farms or in factories. Work the average Italian is unwilling (or unable) to do, in part because of the low wages and again, lack of career prospects. This is the work that immigrants have been doing in Italy for years now. Whether it was the Romanians or Polish in the early noughties to Sub-Saharan africans of recent years.
The simple truth is Italy needs immigrants, more than most other European countries. If only to pay their taxes to support the pensions of the older population. This is a truth that the Democratic Party espoused, but was laughed at by the general populace who cite arguments similar to the one you made. But it's true, even WITHOUT the emigration of Italy's youth, Italy has an aging population due to the low birth rate and extended life expectancy even more extreme than in other European countries.
Short answer. The emigrants and the immigrants are looking for different jobs.