The Sefer HaIkarim 1:15 and the Avnei Eliyahu from the Gra"h on the siddur explain that "da'as" is the "מושכלות הראשונות" - the simple matters, the initial innate knowledge that a person has. This knowledge, which is similar to instinct, is given to man.
Binah, on the other hand, is when someone extrapolates from that primal body of information and forms new understandings.
The Sefer HaIkarim explains that thus da'as is paired with Adam, man, as it is the lowest common denominator and everyone has and uses it. Binah, however, is a higher level, and requires "natural" learning, i.e. personal effort to understand, which only Enosh reaches (Maharal Derech Chaim 3:17 demonstrates this implication of Enosh from Tehillim 55:14 - ואתה אנוש כערכי). Therefore, binah goes a step further and requires "teaching" and "learning."
(Up until here primarily from the Sefer HaIkarim)
However, binah (and all Torah knowledge) still requires a gift from Hashem. The requisite "learning" is on top of that which it must be given by Hashem. Torah knowledge is not naturally learned - it is Divine knowledge, which must be given by Hashem. R Weinberg demonstrated this from the famous statement of Chazal (Eicha Rabba 2:13) - חכמה באומות תאמין תורה באומות אל תאמין - "If you are told that there is wisdom in the Nations, believe it, but Torah in the Nations, do not believe it" - Torah is different than "wisdom" and is not just another body of information. Similarly, the Alei Shur points out that the Gemara in Megillah 6b says "יגעתי ומצאתי תאמין" - "If someone says they put in effort and found, believe them" - even once you put in your effort, Torah knowledge is still "found" - it is something that, in a certain sense, you stumble upon, because its attainment is not the natural result of your efforts.
In summary, "binah" necessitates the higher level of "melamed," but that is in addition to the baseline requirement of "chonein," which all knowledge requires.