The speaker states that anyone who believes in structuring emotion in logic and order will never fully experience that emotion. The emotion must be felt first. If the emotion is filtered through a logical or intellectual medium, it becomes less significant and less sincere.
The speaker uses grammatical structure to signify this structure and order. Cummings is known for mixing word order and ignoring the traditional rules of grammar and traditional styles in poetry. One who pays attention to syntax is too concerned with order; not concerned enough with feeling. Life is not as ordered as a paragraph. Life is full of tangents and word fragments. Life is more like poetry than prose. Therefore, the flutter of eyelids is a more natural, spontaneous, genuine and sincere gesture than something that is logically constructed like the best gesture of his brain.
Emotion is more spontaneous than logical thinking. Words free of syntax are less restrained. The speaker is saying the same thing about emotion. Free of logic, emotion is less restrained.