opposite vs. contrary
I guess that "opposite" doesn't always mean, for example, some two groups are arguing/fighting on something.

It just means two opinions on some topic/issue. Am I right?

On the other hand, "contrary" always refer to opposite two groups that are negative on each other's opinion.

Plz, correct me if I'm wrong. (Also If I've made grammar mistakes in the sentences, correct me, please:))

If my understanding is right,
My opinion is quite to the contrary.(I don't agree with you completely.)
My opinion is quite to the opposite.(I respect your opinion but I have a different point of view.)

Would this interpretation work?:)

Question

opposite vs. contrary
I guess that "opposite" doesn't always mean, for example, some two groups are arguing/fighting on something.

It just means two opinions on some topic/issue. Am I right?

On the other hand, "contrary" always refer to opposite two groups that are negative on each other's opinion.

Plz, correct me if I'm wrong. (Also If I've made grammar mistakes in the sentences, correct me, please:))

If my understanding is right, 
My opinion is quite to the contrary.(I don't agree with you completely.)
My opinion is quite to the opposite.(I respect your opinion but I have a different point of view.)

Would this interpretation work?:)

Answer

It is not that the two words have different meanings, but that they are used in different contexts.
For example, a phrase often used is  'on the contrary', meaning  'I disagree with that [something which has just been suggested], and then you will state your opinion.
'English is an easy language to learn.'
'On the contrary, I think it's very difficult.'

'Opposite' can refer to anything for which there is an alternative :
on the opposite side [of a road, place, point of view, argument]  e.g. 'He takes the opposite side' ;  'My opinion is quite the opposite' [in a discussion, debate, argument]

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