私にそれがよく分かりません
In this sentence, 私 is said to be a dative subject and それ to be a nominative object. If they are named after their case markers, I wonder why we cannot simply regard に and が as a nominative marker and an accusative marker respectively? There seems no nominative-ness in それが to me, same thing for 私に.
There are a couple points that cause some common confusion for English-language learners of Japanese, particularly for these verbs like 分かる and 出来る.
Part of the problem is that the verb here describes a quality of a thing, and not an action by a person.
In the comments, there is a description of が in this sentence as an object marker. This それ is only an object in English, after translating. As Japanese, this それ is the subject of the intransitive verb わかる.
わかる derives from verb わく ("to split, to come into pieces"), as the spontaneous or potential, describing that a thing "comes apart" on its own or "can come apart". This developed idiomatically to mean something closer to the English phrasing "it is apparent how it fits together".
The subject in Japanese is the thing that "comes apart". A better gloss in English, in order to show more clearly how the Japanese verb functions, might be "to be understandable".
The に in the Japanese doesn't mark a "dative subject" so much as it marks the agent of the action, exactly like in passive constructions. Just like in the English phrasing, "it is understandable by me". Or, to use the phrasing further above, "it is apparent to me how it fits together".
