I can see how learning in chevruta pertains clearly to Halachah. Halachah is an objective system that boils your subjective world down into step by step instructions for how to serve HaShem through living your daily life. It's easy to gloss over the Halachah and misunderstand how to apply some objective ruling to your subjective world. By learning with a chevrutah, you need to apply the same objective ruling always to at least two subjective worlds, this increases the chances you will correctly understand and internalize the halachah.
When learning the written Torah, or the hidden, nistar, Torah, the goal is very different. The goal of the nistar is to connect to HaShem. The goal is admittedly insurmountable from the outset. HaShem is beyond us in every imaginable way. Still, through our nistar studies we can attain a form of closeness, a relationship with HaShem.
In such an instance, it is very hard to learn with someone else. For a good example, try and explain to someone else how to do something on their computer over the phone.. You are looking at your desktop, and they are looking at theirs and you are telling them what to click and where. (I'm sure most people who can find this blog have had this experience in one instance or another) It is tremendously difficult and requires a lot of patience. The more you use your computer, the more specific and customized it becomes, the more difficult it is to relate to someone else's computer. The more personal your relationship to HaShem through the nistar, the more difficult it becomes for two people to study together.
This is how it always seemed to me anyways. But the more I thought about it the more I realized how much more there really is to it:
When two people come from a very close spiritual connection, from the same soul root, then since their connection with HaShem has many similarities it is easier to learn with them and helping them to connect actually helps you to connect. On an even deeper level all of Bnei Yisrael is connected spiritually and learning with any member of Bnei Yisrael and helping them to connect to HaShem bridges and strengthens and deepens your own connection.
This is a very high level of understanding. But, when we can relate to our fellow Jew as a part of ourselves, carved from the same source, then learning with them can be transformed from a chore to a very high level of relating to HaShem. A level above relating directly, as we learn in the Tanya in chapter 32 (לב) that truly loving HaShem is loving what He loves most, Bnei Yisrael. Giving and sharing with Bnei Yisrael allows us to get even closer to HaShem than trying to pursue HaShem directly.
This is why Gemilat Hesed is tantamount Torah learning, and Teshuvah, and Tefillah. (See Pirkei Avot) Because through the Hesed that we do with Bnei Yisrael we can attain a closeness that isn't possible through relating to HaShem directly. (The goal of Torah, Teshuvah, and Tefillah)
As we know, the highest Gemilut Hesed, the highest Tzedaka enumerated by the Rambam is teaching someone to help themselves. What could be higher than learning with another Jew and helping them to get closer to HaShem directly? That it brings us closer to HaShem shouldn't hurt either.
This understanding of Chevruta and learning for the sake of raising all those learning closer to HaShem is often demonstrated in the Zohar. In the Gemara every learning is about hearing. Come and hear. In the Zohar, there are many descriptions that use words like "over there," "on this side," and "like so." One way to understand what is going on in the Zohar is to understand that when learning and discussing the Zohar they were actually in the midst of a common mystical experience of the heavenly realms and the underlying structure of the world. This way, when they pointed to or gestured at things, it was to illustrate the idea being discussed. Outside of this common mystical experience it is much more difficult to understand the explanations according to all of their implications and manifold possibilities.
Sinat hinam, free hatred of our fellow Jews brought about the destruction of the Beith HaMikdash, without being able to come together and unique in goals of holiness like Torah learning, we can't repair that breach.
B'ezrat HaShem we should all merit to bring ourselves, those around us, and all Klal Yisrael closer to HaShem through Torah learning in chevrutah.