Let's say there's someone you don't get along with and can't stand.

Literal

Self [with-と] spirits [subject-が] not-match, not-liked, people [subject-が] exist [supposing-とします].

A hypothetical set-up. 気が合う/合わない ('the spirits match/don't match') is a fixed idiom for 'getting along / not getting along' with someone — literally 'the ki matches,' using the same 気 concept seen in 気が強い and 気が立つ earlier. 気が合わない = 'don't get along,' 'clash personality-wise.' いけ好かない ('can't stand,' 'distasteful') is a compound: 行け (variant/emphatic prefix) + 好かない (negative of 好く, 'to like') = 'positively dislikable.' A slightly old-fashioned colloquial expression. ~とします ('let's suppose X,' 'let's say X') is the standard frame for introducing a hypothetical scenario.