The two friends do not match eye to eye when it comes to their business rivalry.
When referring to agreement or common viewpoints, use the expression see eye to eye.
see eye to eye
The idiomatic expression see eye to eye means to agree or have the same viewpoint, which fits the context of the sentence regarding the rivalry between the friends. - Option (A) meet eye to eye is incorrect as it implies a literal meeting of eyes rather than agreement. - Option (B) see into each other's eyes is not an idiomatic expression and doesn't fit in the context. - Option (C) look into each other's eyes is also incorrect in terms of meaning, as it doesn't fit the idiomatic usage of agreement. - Option (D) see eye to eye is the correct idiom meaning to agree, making it the right choice.
The original sentence uses a literal-sounding phrase, "match eye to eye," where an actual idiom is intended, so distinguishing literal descriptions of eye contact from the genuine idiom of agreement separates the options.
Since only option D is the genuine, standard idiom for agreement, it is the correct replacement.
Hence, the correct answer is Option D.