I don't know why the bible says it but I know 2 interpretations the WTS uses
1) Lev. 18:19, 20:18---the menstrual renders women incapable of sane thought. "vicissitudes"
*** it-2 p. 1154 Vessels ***Women are designated as the “weaker vessel.” Therefore, Christian husbands, by taking into consideration their wives’ physical and biological limitations, as did Jehovah in the Law given to Israel (Le 18:19; 20:18), act “according to knowledge, assigning them honor as to a weaker vessel, the feminine one.”—1Pe 3:7.
*** w51 5/1 p. 279 Making a Success of Marriage ***Ah, yes, live with your wife according to knowledge of God’s commands and with understanding of his fundamental laws of nature. Consider the biological constitution of the female, her limitations, her cycles, her vicissitudes, which greatly affect her mentalprocesses, disposition and temperament. God does not overlook these feminine restrictions; neither should husbands. (Lev. 18:19; 20:18) You husbands, look upon your wives as if they were delicate instruments, finely balanced, and give them the same gentle treatment you give the delicate organs of your own body. Showing love and tenderness is not displaying masculine weakness, nor is it showing reverence. Perish the thought! “Assigning them honor as to a weaker vessel” has nothing to do with the wrongful practice of setting women above men on a pedestal of worship. Bestowing tender affection upon a wife causes her to respond with “deep respect for her husband”, and this is the way it should be.
*** w80 4/15 p. 22 par. 18 ‘A Love As Strong As Death’ ***By taking into consideration her physical and biological limitations, as did Jehovah in the Law given to Israel, the Christian husband will act “according to knowledge,” assigning his wife “honor as to a weaker vessel, the feminine one.”—Lev. 18:19; 20:18; 1 Pet. 3:7.
2) in later years, that in general women are physically weaker than men