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We must cultivate attractive qualities of disposition and behavior if we are to draw out the best which the society of our fellows has to offer

About the part in bold, is it:

(1)the best+ the society of our fellows has the best to offer
or
(2)the best+the society of our fellows has to offer the best

?

I tend to think it's #1, but I'm not sure on this one.
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Comments  
I may be misunderstanding your analysis, but I don't think it's either one.

I go into a dress shop. "I want to buy the best dress you have for sale. Bring out the best which your store has to offer."
Well, my question is, is it:

X+S has X to do→X (which) S has to do

or

X+S has to do X→X (which) S has to do

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Excellent comparison.

The best that our fellowship is able to offer, or will be able to offer, if we all do our best to make it that way.
 So you think it's the latter: 'X+S has to do X'?

Hmm...so the society MUST offer the best?? 
Please forgive me, Taka. Suddenly I'm studying English as a foreign language. I've tried figuring out what your symbols mean, and I've failed.

I look forward to enjoying the rest of this as a spectator. - A.
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AvangiPlease forgive me, Taka.  Suddenly I'm studying English as a foreign language. I've tried figuring out what your symbols mean, and I've failed.
I look forward to enjoying the rest of this as a spectator.  - A.
S is the subject of a sentence and X is just a thing. 
Okay, I get it. You're considering the possibility that "has to" = "must." A big negatory on that! "Has to offer" = "Has for sale." NOT "Has to offer" = "Must sell." (They guts to do it!)
Same idea here except that I wonder the offer of the sentence in original is really about selling something. 
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