IPA: /ˌdɪsəˈɡriːmənt/
KK: /dɪsəˈɡrimənt/
A situation where people have different opinions or beliefs and do not agree with each other.
There was a disagreement between the two friends about where to go for dinner.
Disagreement is formed from "dis-" (meaning apart) and "agreement" (from Latin "ad-" meaning to, and "gratus" meaning pleasing). The word describes a state where people are not in agreement or are apart in their opinions.
Think of being 'apart' ('dis-') from a 'pleasing' agreement — that's why disagreement means not being in harmony.