Help with SAT Official Practice Test 5 Reading Question 15

I’m having trouble understanding the solution to this question

“It was designed that the mode of gaining influence and of exercising power [of men and women] should be altogether different and peculiar…”
Question 15: "Peculiar most nearly means?

The official explanation is:
Choice C is the best answer. When describing how men and women can influence society, Beecher says the ways they can do so “should be altogether different and peculiar” (lines 11-12). In the context of the “altogether different” ways men and women can influence society, the word “peculiar” implies being unique or distinctive.
Choices A, B, and D are incorrect because in the context of the “altogether different” ways men and women can influence society, the word “peculiar” suggests something unique or distinctive, not something unusual and odd (choice A), unexpected (choice B), or rare (choice D).

I find it hard to accept the answer is C. Since the sentence already has the word “different”, if peculiar were to mean distinctive than the word “peculiar” in the original sentence would be redundant. Seeing that both adjectives were used, peculiar must have had a different meaning than “different”!

Can any CCers help me out here? What’s the right way to do these questions anyway, substitute the answer choice into the original sentence?

One meaning of “distinctive” is:
“characteristic of one person or thing, and so serving to distinguish it from others.”

In everyday language, we usually use “peculiar” to mean “strange” or “unusual”. But in formal English, “peculiar” often means “belonging to one person or group.” When it has this latter meaning, it is a synonym for “distinctive”.

This sentence says that the mode of influence of women is characteristic of women and distinguishes them from men.
So “peculiar” = “distinctive”.

You need to consider all the different meanings of the words to answer these questions.

It sometimes happens on questions rated at lower to mid-level difficulty that the question will contain a clue to the correct answer.