{A} - INCORRECT; "it" is not needed.. we are already talking about human mind; "as a way of solving" is wordy.. "to solve" is concise usage;
{B} - CORRECT
{C} - INCORRECT; meaning issue by introducing ", instead of a "blank slate,"; "it" is not needed
{D} - INCORRECT; "as a way of solving" is wordy.. "to solve" is concise usage; "it being" is not needed; meaning issue
{E} - INCORRECT; "as a way of solving" is wordy.. "to solve" is concise usage; idiom issue rather than x Y is correct usage;

A: We can easily determine that A is much wordier than B. Though, it has another mistake: its structure. Let's strip the sentence to its core:
Psychology holds that ..., but instead that... Doesn't it look strange? If we are going to connect two relative clauses with "but", we should put "not" not within the first relative clause, but in front of it:
Psychology does not claim that it invented the science(,) but that it helps understand the human mind.
Psychology claims not that it invented the science(,) but that it helps understand the human mind.

B: correct and smooth: "the human mind is not X but instead comprises" -- the perfect parallelism (not X but Y) is not required; the sentence is good as it is.

C: "Psychology holds that the human mind, ..., it comprises ..." We can get rid of the phrase set off by commas (such phrases are not essential to the sentence). We get: "the human mind it comprises" - two subjects! This is definitely a mistake. The second mistake is that Present Perfect shouldn't be used with a specific timeframe: millions of years ago. The "ago" is a sure indicator of Past Simple.

D: "rather than it, the human mind comprises" (we can omit "being a 'blank slate'" because it is only a modifier of "it") -- no parallelism whatsoever. "Rather than"-structure required some sort of parallelism:
Rather that Mary, Peter should go.
I bought cheese rather than rice.
With verbs situation is more complicated, but we shouldn't worry about it, because "it" (a word after "rather than") is a pronoun and plays the role of a noun. Here "it" is parallel to "the human mind", but at the same time "it" logically stands for "the human mind", so they are the same thing! (Mary and Peter are different people, and cheese and rice are different products in my examples above)
The second problem with D is that "the human mind" comes after its pronoun "it". Usually it is possible on the GMAT when there're no legitimate antecedents for "it" before the pronoun (OG13, problem 104). On rare occasions this rule can be "broken", but there must be a good reason to do it (to avoid repetition of words, for example, as in problem 8 of Paper Test Code 55, Section 6). Here this rule is violated ("it" can refer to "psychology") without any reason.
The third reason is that the GMAT doesn't like "being" if it's used as a participle. There's a very good explanation by Ron about it somewhere.

E: "that rather than the human's mind being X" -- this relative cause is incomplete. "Being" here is a gerund, so it plays the role of a noun. We get: rather than [being]. So what? The thought is completed, of course, in the second that-clause, but it is a mistake. We should complete our "rather than"-thought where we started it (in the first that-clause).
The second mistake is awkwardness. "Something's/somebody's being/doing" provides a hint that the answer is incorrect. Though, good as it is, it's also not a 100% rule - see the problem 120 in OG13 where "human being's burning" was in the correct answer.