Love is like a baby: it needs to be treated tenderly.

Love is not a person we can see or touch. I think the love used in the proverb refers to the thing or person whom we love. In other words, it refers to the object of our love or the object of our affection.

When you love someone, it is almost natural that you would treat the person softly and tenderly, and would not treat the person rudely. Being tender toward someone is like being patient, kind, sympathetic, harmless, etc. toward the person.