Difference between compatible and agreeable

what is the difference between compatible and agreeable?

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For people, agreeable = to your own liking or feelings or nature while compatible = having similar disposition and tastes. Agreeable sets the other person to matching your own druthers, while compatible asks for a meeting halfway. That’s briefly how I see it.
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Dear Sir,

Please read:

“Agreeable” sets the other person to matching your own druthers, while “compatible” asks for a meeting halfway.

Please tell me the meaning of drutherand that ofmeeting halfway. (I can’t find the answers in my dictionary)

Many thanks
Quoc

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I’d say the word “druthers” is quite well-known in the US as is the phrase: “If I had my druthers…” Someone’s “druthers” refers to what someone’s free choice would be. This word seems to have arisen from “would rather”.

The expression “meet someone halfway” means to “compromise (with someone)”.

By the way, there may be a difference between AmE and BE in the phrasal verb “set someone to do(ing)”. In MM’s sentence, the word to is used as a preposition and it is therefore followed by a gerund.

Here is another an example of “set someone to doing something” (taken from the Princeton University website):
Nothing in particular set him to thinking about this…
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Dear teachers,

1/

a.Nothing in particular set him to thinking about this.
b.Nothing in particular set him to think about this.

All (a) and (b) are correct in grammar and have the same meaning?

2/
c.“Agreeable” sets the other person to matching your own druthers.
d.“Agreeable” sets the other person to match your own druthers.

All © and (d) are correct in grammar and have the same meaning?

3/You wrote:
This word seems to have arisen from “would rather”.

What does “to have arisen from” mean?

Quoc

Many thanks, teacher.

Tung Quoc