The Ran (“U-shevuous”) on Amud Aleph uses an interesting phrase, לא ירדתי לסוף דעתו which literally means, “I was not able to descend into his understanding (or opinion)”, in other words, “I couldn't understand his reasoning”.  It is interesting to use the word descend when it comes to understanding.  Actually, a similar but opposite phrase is used in Midrashic literature (for example, see Bereishis Rabba 44;23), “Alah Be-daato, which means “He thought of something.”  There is also similarly, “Alah Be-machashavto”, (see Midrash Tanchuma Sheminin 8:3 and Pirkei De-Rabbi Eliezer 11:11.)  This is not a contradiction, as thinking of an idea or having an opinion, is different than trying to understand another opinion.   Also, many of the midrashic uses of “Alah” are in reference to God’s thinking, and perhaps out of respect, a term of going up in thoughts is used.

In terms of the phrase “ירדתי לסוף דעתו” it is used by other Rishonim as well, see Ramban Bava Metzi’a 5b and Ritva Kesuvos 55a.

Why do we use the connotation of going down when we are trying to understand a person’s thought process?  If anything it would be more respectful to say, “Lo Alisi al Daato”, “I have not been able to ascend to understand his opinion”?

I believe the source of this phrase comes from Mishley (20:5):

מַ֣יִם עֲ֭מֻקִּים עֵצָ֣ה בְלֶב־אִ֑ישׁ וְאִ֖ישׁ תְּבוּנָ֣ה יִדְלֶֽנָּה׃

The designs in a man’s mind are deep waters, but a man of understanding can draw them up

Meaning to say, as there are deep wells of water unseen on the surface, so too in every person there is a reservoir of great knowledge that needs to be tapped.  Perhaps this is what is meant by the Gemara (Niddah 30b) which tells us that we learn the entire Torah in the womb, and all learning is really re-learning.  (Compare this to Plato and Socrates’ Meno 82b–85b, as they also had a tradition that the immortal soul knows everything and only has to re-learn it.)  Related to this idea about wellsprings of knowledge, here is what Chovos Halevavos says in his introduction, referring to knowledge and intuition in middos:

ואמר חכם אחר יש מן החכמה מה שהוא צפון בלבות החכמים כמטמון הנסתר אשר אם יסתירוהו לא ישיגנו אדם וכאשר יגלוהו לא יעלם מאדם יושר אמריהם בו וזה כמו שאמר הכתוב (משלי כ) מים עמוקים עצה בלב איש ואיש תבונה ידלנה רצה לומר כי החכמה תקועה בתולדות האדם וטבעו ובכח הכרתו כמים הטמונים בלב הארץ. והנבון המשכיל ישתדל לחקור על מה שיש בכחו ובמצפוניו מן החכמה לגלותו ולהראותו וישאבנה מלבו כאשר יחקר על המים אשר במעמקי הארץ

A third Sage said "there is wisdom which lies hidden in the hearts of the wise, like secret treasure. If they conceal it, man cannot discover it. If they reveal it, man cannot deny the correctness of their words regarding it. And this is as Scripture says "wisdom in the heart of man is like deep water, but a man of understanding will draw it out" (Prov. 20:5), i.e. wisdom is innate in a man's being, in his nature and faculties of perception, like water that is hidden in the depths of the earth. The intelligent and understanding individual will strive to investigate what is in his potential and inward faculties in order to discover and expose this wisdom, and will draw it forth from his heart, just as one searches for water that is in the depths of the earth.