Those who are associated in their lives, tend to become assimilated in their character. In the present closeness of association between the sexes, men cannot retain manliness unless women acquire it.
She wants women to become manly so that their femininity doesn't rub off on men. She is assuming first that femininity is something undesirable and unworthy for women and second that women can simply "acquire" masculinity.
Put another way, she wants to abolish sex distinctions - the differences between men and women - in favour of a single masculine identity for both men and women.
Nor was this an unusual position for the pioneer feminists to take. Mary Wollstonecraft wrote in 1792 that:
A wild wish has just flown from my heart to my head, and I will not stifle it, though it may excite a horse-laugh. I do earnestly wish to see the distinction of sex confounded in society ... For this distinction ... accounts for their [women] preferring the graceful before the heroic virtues.
Again, we have the desire to abolish "the distinction of sex"; men and women are to follow equally the masculine way of life - the more graceful feminine virtues are to be jettisoned.
It is ironic that such women came to be labelled feminists when they were so obviously hostile to the feminine.
There were antifeminist women in the 1800s who took a different view. Eliza Linton was the first full-time staff journalist in England in the 1840s. You might therefore assume that she would be a supporter of the early feminist movement. In fact, she was highly critical of it. She objected to the anti-feminine aspect of feminism, as well as its hostility to men.
For example, in the 1860s Eliza Linton addressed feminists as "you of the emancipated who imitate while you profess to hate". She criticised feminists of this era as "the bad copies of men who have thrown off all womanly charm".
Nor did Eliza Linton accept that feminine women were a danger to masculinity. She thought the opposite was true:
with the increased masculinity of women must necessarily come about the comparative effeminacy of men.
This, I believe, is a more reasonable view. A feminine woman is much more likely to engage a man's masculine instincts. If a woman behaved exactly like a man, then to whom would a man's masculine drives and instincts be directed? The complementarity between the masculine and feminine would be lost.
Eliza Linton also disagreed with Harriet Taylor Mill that women could simply "acquire" masculinity. Eliza Linton didn't see sex distinctions as unnatural categories that we could manipulate according to our own preferences. She thought they had some basis in nature and that they helped to guide human action:
I think now, as I thought then, that the sphere of human action is determined by the fact of sex, and that there does exist both natural limitation and natural direction.
Modern science has vindicated Eliza Linton's position. We know more now about the biological distinctions between the sexes that are hardwired into our physical nature, including different exposure to sex hormones and differences in the structure of the brain.
One final point. It is odd, to say the least, for a heterosexual man or woman to wish away sex distinctions. Unless we make a tremendous effort to subdue physical desire and emotional responsiveness we are not ever going to enthusiastically urge women to "acquire masculinity".
Harriet Taylor Mill's philosophy would only suit those who thought of themselves as disembodied, abstracted intellect or character - as the most extreme of intellectual types might do. But this reflects a limitation on their part that the rest of us would be unwise to fall in with.