Did Misogyny Influence Jared Loughner?

Did congresswoman Giffords' gender play a role in the way Loughner selected his victims? Some suggestions that it might be so:

Federal investigators found the words "Die Cops" and "Die Bitch" scrawled on a letter from U.S. congresswoman Gabrielle Giffords's office in the home of the shooting suspect, a sheriff's department official said Tuesday night.

And

At a small local branch of a major bank, for example, the tellers would have their fingers on the alarm button whenever they saw him approaching.
It was not just his appearance — the pale shaved head and eyebrows — that unnerved them. It was also the aggressive, often sexist things that he said, including asserting that women should not be allowed to hold positions of power or authority.
One individual with knowledge of the situation said Mr. Loughner once got into a dispute with a female branch employee after she told him that a request of his would violate bank policy. He brusquely challenged the woman, telling her that she should not have any power.

And:

Later that day, in an even more horrifying post titled "Why Rape?", he claimed that college women liked being raped.  He wrote, "there are Rape victims that are under the influence of a substance. The drinking is leading them to rape. The loneliness will bring you to depression. Being alone for a very long time will inevitably lead you to rape."

That Loughner had misogynistic feelings seems pretty clear. It's not equally clear if those played the major role in how he picked whom to kill. At the same time, as Tom Scocca notes when discussing the above New York Times quote about Loughner's behavior at the bank:

Suppose the story said that Loughner "grew contemptuous of Jews" and went around "asserting that Jews should not be allowed to hold positions of power or authority," even blurting anti-Semitic remarks to strangers. And then he went out and shot Giffords, a Jewish congressperson. Would his motives have seemed quite so incomprehensible? Would the Times have waited 17 paragraphs to get around to that fact?

Scocca has a point. Misogyny of the type Loughner demonstrates in those quotes is so prevalent on the Internet, in particular, that we don't really see it for what it is: An expression of hatred towards one group of individuals.