This is a jukugo word that uses the on'yomi readings of the kanji. You haven't learned this reading for 右, so here's a mnemonic to help you:

Those in the right wing love eating uni (う), not because they like the taste, but because uni is expensive. Picture some right-wing people in your mind right now and watch as they try really hard to pretend they like eating uni as they shovel buckets of it down their throats.