Use the adjective incompatible to describe things or people that are too different to get along. When paired with someone you can't work with, don't criticize or get mad. Just say, "We are incompatible."
Put together the prefix in- and the suffix -ible and what do you get? "Not able." The center of incompatible comes from Latin, compati, or "suffer with." So think of incompatible as a way to describe something you simply are not able to suffer — there's too much conflict. Things can be incompatible just like people. Just try hooking up an incompatible piece of hardware to your computer — it won't work because it was designed for a different system.