Despite the technically-correct radical being ⺼(“meat”) as described in this entry’s glyph origin section, 有 is associated with the radical 月(“moon”) in dictionaries for historical reasons and is likewise written as if it contained the 月 radical, i.e. it has 二 instead of 冫 inside of 冂.
Ideogrammic compound (會意) and phono-semantic compound (形聲, OC *ɢʷɯʔ): phonetic 又(OC *ɢʷɯs, “hand”) + semantic ⺼(“meat”) – a hand holding meat, hence “in possession of”. The hand shape has been significantly abstracted; compare 右 (OC *ɢʷɯʔ, *ɢʷɯs).
Alternatively, the graph was perhaps originally intended for the word 醢 (OC *qʰɯːʔ, “minced pickled meat”), which also has the 又 (OC *ɢʷɯs) element as phonetic.
Shuowen Jiezi and other ancient sources have erroneously analyzed the character as a phono-semantic compound (形聲, OC *ɢʷɯʔ): phonetic 又(OC *ɢʷɯs) + semantic 月(“moon”). Shuowen Jiezi defines 有 as "不宜有也" ("[to have something that] not should be had"), citing the Spring and Autumn Annals (春秋傳): "日月有食之" ("There are solar and lunar eclipses"). As eclipses were not auspicious to the Chinese, they were "something that should not be happening". The 月 component alludes to the inauspicious lunar eclipse.