Reading and writing in two languages

Hi! I am Italian, my husband is German, we have three kids, they speak both languages very well. The eldest just started primary school and the teacher told me off because I signed a note for Alex "mamma" (italian) and not "mama" as in German. She told me that I am not supposed to teach the child how tro write in Italian otherwise he will only be confused and will not learn anything. She said that, for instance, when the kids learn English starting from class 1 they do not learn to write till class 3. But I think it is completely different, I mean, English is for them a foreign language, while Italian is Alex's mothertongue (and German his "fathertongue"...) and as he know the difference in the spoken language should have no problems in writing both languages.
>What do you think? Any first hand experience? Any teacher here to give me an advice?