I have quite advanced knowledge of Italian and still there is a very "stupid" question that bothers me. When Italian say - Parlo l'italiano or parlo il tedesco - I understand that it is a masculine noun but cannot figure it out in my mind how to translate it into English, since in English it is an adjective. In other words, why must it be masculine noun, why not Parlo l'italiana, I mean the lingua italiana, the italian language?
Ciao, that is not a stupid question at all, considering you are an english speaker.
The gender is something we inherited from the past, from the Latin language which also had a neutral gender, and from the previous ones such as Greek. Nowadays romance languages only have the feminine and masculine gender except for Romanian (but many neutral words are still present in my language, with the feminine or masculine form though).
As for your example:
Parlo (l') italiano. → I speak Italian.
In both cases the name of language is an noun, not an adjective. We can find two main differences:
italian is a noun without gender while italiano is categorized as a masculine noun (as you wrote) and it's invariable, since it doesn't have a feminine form nor a plural one (uncountable). This happens only when you're using this noun referring to people e.g. L'italiano/L'italiana/Gli italiani/Le italiane.
italian doesn't take a definite article while italiano can take it or not, in the colloquial language often it's dropped using verbs parlare/studiare.
You could turn the noun italiano into an adjective and this way you should conjugate it following gender/number of nouns to which it refers e.g.
Io parlo perfettamente la lingua italiana.
Io sono italiano/a.
I programmi italiani sono interessanti.
About languages, this "feminine change" because of the addition of lingua is more evident with nouns ending in -o, since the ones with -e continue keeping this letter at the end when they become feminine adjectives too, they are invariable (e.g. l'ingles-e/la lingua ingles-e).
Finally, more in general consider that many nouns ending in -o but also in -e can be masculine. Here is a discussion about this if you need:
Italiano can be many things:
Italiano/italiana can be an adjective. An adjective's gender matches its noun:
Marco è italiano. Anna è italiana.
Italiano can be a noun. As a noun it is gender invariable:
Marco parla italiano. Anna parla italiano. Noi parliamo italiano.
I'm a native speaker. You must accept the fact, for every language you must use the masculine article, there's no exception. Try to think that what is implicit is "linguaggio", which is masculine, and not "lingua"if this can help you.