"Strong and independent" in this case is a sarcastic epithet, for example. "power" and "independence" are expressed in the establishment of a dozen mocked surrogates of the man, on which you can move love-care and comfort yourself with illusions of self-careful, self-delicate, self-needed and self-loved.

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Even if it is (in my whole life I have not met any real woman with 10 cats and without a man, but let’s say) – you what?
Is it intolerably bombarded by the fact that one in three billion women on the planet fails to fulfill their primary duties of serving men? Are you afraid that you won’t get women? Or what? Where is so much emotion, anger, contempt, sarcasm, the desire to express your thoughts on the Internet - to some abstract unfamiliar women?

One of them stole your cat to "please yourself with illusions"? Or does your penis get 1 cm shorter every time someone gets another cat?

An adult, unfamiliar to you person has made a conscious decision - to live with cats, and with men only to meet for a fuck (and maybe sometimes something else) or even not to meet at all - what's up to you? Will the sky fall to earth? Or are you concerned about her personal happiness? So don’t worry, she’s happier than those who live with “mirror disease, pimples and gigabytes of porn!” And sex with her happens more often, but this is far from the most important moment in it all.