speak language

speak (one's) language

To say something or communicate in a way that aligns with one's preferences, desires, motivations, etc. A: "Look, I know all this technical jargon is pretty boring. Why don't we finish early for the day and go out for pizza?" B: "Oh yeah, now you're speaking my language!" A: "I'm a little worried about pitching my idea to the board of directors tomorrow." B: "Just focus on how your plan will boost profits, and you'll be speaking their language."
See also: language, speak
Farlex Dictionary of Idioms.

speak someone's language

Fig. to say something that one agrees with or understands. I gotcha. Now you're speaking my language. Mary speaks Fred's language. They get along fine.
See also: language, speak
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.
See also:
  • speak (one's) language
  • speak someone’s language
  • run (one's) own show
  • run one's own show
  • know (someone or something) like a book
  • know like a book
  • get past
  • get past (oneself)
  • (one's) (true) stripes
  • (one's) true color(s)
References in classic literature
The pen employed in finishing her story, and making it what you now see it to be, has had no little difficulty to put it into a dress fit to be seen, and to make it speak language fit to be read.
The Fortunes and Misfortunes of the Famous Moll Flanders
(http://www.ibtimes.com/mowgli-girl-found-living-monkeys-india-walks-all-fours-doesnt-speak-language-2522022) Read: 'Mowgli' Girl Found Living With Monkeys in India Walks On All Fours, Doesn't Speak Language
'Mowgli' Girl Raised By Monkeys in India Still Not Identified
Our ability to speak language is an inborn characteristic of our species.
THE COMING AGE OF TALKING COMPUTERS
Specialists in communication disorders address a wide range of clinical and theoretical questions regarding children with language disorders who speak languages other than or in addition to English.
Multilingual Perspectives on Child Language Disorders
David Laws, Lib Dem spokesman for schools, warned of weakening students' ability to actually speak languages.
'Stressful' oral tests face axe
For instance, Latin America generally refers to all countries south of the United States that speak languages descended from Latin (mostly Spanish, but also Portuguese and French).
MAPMAN