The Language "Magic" within the language system is NOT a conversational language. It is a combination of Arcane words used to cast magical spells and perform magical rituals. Although when speaking the "magic" language, the system allows for the words to have actual meanings, the language itself has many words that are known but there is no grammar or pattern to the words which would allow it to be used as a spoken communication language.
Furthermore, when thinking of the language of Magic. The arcane words themselves carry power when used by a caster of arcane spells. As such, NO caster with an intelligence greater than 2 would ever attempt to communicate using arcane words. Doing so would be far far to dangerous. Speaking the words of magic would bring too much of a possibility of accidently casting a Destruction spell or a Fireball at your intended listener.
From here on out, the language of Magic is not authorized to be used as a conversational language.
You can feel free to attempt to use it as one, but if a DM sees it do not be surprised to find yourself accidentally summoning a very angry Balor Warlord or casting a Finger of Death at your best friend or familiar