Phonosemantic compound. 羊 represents the meaning and 我 represents the sound. In ancient China sheep (羊) were associated with goodness and beauty, which is why 羊 is a component in characters like 美 (beautiful), 善 (benevolent), and 義 (justice).
義 and 我 don't sound similar in modern Mandarin due to historical phonetic changes. They were more similar
in older Chinese.
Character Evolution
Oracle Bone~1250-1000 BCBronzeEarly Western Zhou~1000 BCBronzeEarly Western Zhou~1000 BCBronzeMid Western Zhou~900 BCBronzeLate Western Zhou~800 BCBronzeLate Western Zhou~800 BCBronzeLate Western Zhou~800 BCBronzeLate Spring and Autumn~500 BCBronzeEarly Warring States~400 BCSealWarring States (Chu)475-221 BCSealWarring States (Chu)475-221 BCSealWarring States (Chu)475-221 BCSealQin221-206 BCSealShuowen~100 ADSealShuowen~100 ADClericalQin221-206 BCClericalWestern Han202 BC-9 ADClericalWestern Han202 BC-9 ADClericalEastern Han25-220 ADClericalEastern Han25-220 ADClericalWestern Jin266-316 ADRegularModern