IPA: /ˌɪnˈkɒnsɪkwənt/
KK: /ɪnˈkɑnsɪkwənt/
Not important or significant; lacking logical connection or sequence.
His arguments were inconsequent and did not support his main point.
Inconsequent → It is formed from "in-" (meaning not) and "consequent" (from Latin "consequentem", meaning following or resulting). The word "inconsequent" describes something that does not logically follow or is not consistent with what has been previously stated or done.
Think of 'not' ('in-') leading to something that 'follows' ('consequent') — that's why inconsequent means something that does not logically follow.