to bring up, to raise
慉 centers on the act of nurturing growth: bringing someone or something up, raising it from a lower to a higher state.
慉 combines the heart radical 忄 with 畜, which likely contributes both sound and the idea of raising or nurturing, as 畜 relates to livestock or rearing.
The heart 忄 beside 畜 (livestock) suggests the care and attention needed to raise animals or bring up children. Picture a farmer's heart full of dedication as they raise their livestock.
For キク, imagine a farmer raising a young chick: the chick's peep sounds like 'kiku', and the farmer's heart is in raising it well.