In English slang "pussy" has several meanings. In it's most benign form, "pussy" can refer to a cat, particularly a housecat kept as a pet. I do not think that is the intended use here.
In it's more vulgar form, "pussy" is also slang for a woman's genitalia. As an extension of that correlation, it is also used as a pejorative to impute femininity when directed at men. Since baser, more backward people in this country still correlate "courage" or "bravery" with being "masculine", pussy (by referring to the most definitive physical feminine anatomy) can also be used to impute cowardice or irrational fear, particularly when directed at men.
Although I've never seen it used in that particular descriptive, it seems clear that mcgeorge is intending to say that by being "a little 'pussy'" we are being cowardly, or in some way cheap and unfair. I have seen other slang terms referring to cowardice used this way (particularly "chicken" or the more vulgar "chickenshit"), but this seemingly is intended to connote a greater degree of cowardice by skulking to a lower, baser vulgarity.
And the unnecessary use of the vulgar, baser speech should serve as a stark reminder of exactly the mentality with which we are dealing, as if the repeated justification of ignorant thinking was not evidence enough.

No, I was calling him a cat.