Once again, to make it clear - the reason why people are suggesting extreme misogyny was a driving factor behind this crime is because it's the reason the killer gave.
So many times one of these mass murder events happens, and when it comes to the "why" we're basically stuck with "we'll never really know", only having to settle for ambiguous clues derived from web search histories or posters the guy had taped up in his room, or conflicting witness statements about what the guy said during the rampage or what not.
Here we have a case where the killer helpfully left this tome behind where he lays out, in excruciating, disgusting, microscopic detail, his thought processes leading up to his killing spree. Women are evil, women are animals, they don't deserve rights, they have rejected me and failed to have sex with me and for that they deserve to die, and I will kill as many of them and the men they've chosen instead of me as I can, he says. And in the face of this incredible and highly concise confession, people insist on second-guessing misogyny as his motive. Either it's "he killed a lot of people and so was obviously crazy, thus his motives aren't really that important" or "a couple of sentences in his pages-long screed against women mentioned also hating the men those women had sex with instead of him, so obviously he hated everyone the same and wasn't especially misogynist". It's amazing. Fantastical. Mind-boggling.
Seriously, if some guy were to shoot up an inner-city school and left a note saying "I shall purge this great white country of all the (expletive beginning with the letter N)s, starting with this school", would his bullets hitting a few of the white students make anyone say "well now wait a moment here, let's not jump to the conclusion that racism had anything to do with what this guy did"?
Bingo. If someone went on a killing spree and cited aryan supremacism as his motive, we'd call that a hate crime. Now this man clearly cited his misogyny as his motive, but MENTAL ILLNESS LA-LA-LA I can't hear you
Very real, and very rare. Misogyny is hatred of women. Not prejudice, not stereotyping...outright hatred.
And homophobia is fear of homosexuals.
Thinking that women are bad at math doesn't make you a misogynist.
Yes, it does. Thinking women are bad at math = thinking women are stupid and inferior to men = contempt towards women = misogyny.
Objectifying women doesn't make you a misogynist.
Depending on context, it might. An individual case of objectifying obviously doesn't, but someone who sees women as nothing more than objects for sex = contempt towards women = misogyny.
Disagreeing with feminists doesn't make you a misogynist.
Having a different concept of sexual equality doesn't make you a misogynist.
If that concept of sexual equality is actually obviously not equality, then yes, it does.
Yet, a lot of people are using the term "misogynist" to mean "chauvinist" or "sexist". I guess those words just don't have the same punch anymore. It appears to me that feminists are using a rhetorical trick to cast their opponents as hateful bigots merely because they disagree with them.
Won't someone think of those poor, poor sexist chauvinists? *violin* Someone who says they don't hate blacks, but wouldn't want their daughter to marry a black man, is still a racist and a bigot. Who cares if they're not "hateful", it still stems from the same toxic ideology (or perhaps ignorance but in this day and age there's no excuse) and still results in all manners of #### towards the targeted group.
I think it's obvious that this guy was a misogynist, if anybody was.
Which raises the question, why are you trying to muddy the waters by splitting hairs over the definition of misogyny?

You agree Rodger was misogynist, so why this semantic debate? Completely irrelevant. But okay, now we can move on at least.
So, while "Not All Men" may be horrible misogynists, "Yes All Women" have been affected by horrible misogynists. Have I interpreted this correctly?
I don't know what you mean by "affected by", so I can't say if your interpretation is correct. There have been many articles written about #yesallwomen, if you're still confused about its origins or purpose I suggest you read them. Or, you know, just read some of the actual tweets...
What do you hope to gain by talking about it?
Silencing women has been part of history since forever and it stifles social progress. What do we hope to gain? Isn't it obvious? Getting people to realize that misogyny isn't as rare as you think it is, even by using your arbitrarily strict definition. Getting people to realize the constant #### women all around the world have to put up with every day of their lives. Getting people to wonder why, if I were to kill a bunch of Jews, it would be a hate crime, but when someone writes an anti-woman manifesto and proceeds with murder, many sweep that under the rug and try to deflect the issue. Getting people to wonder why so many still think of women as someone's wife, daughter, sister (even among those who use that "positively", e.g. "how could he treat women like that, what if it were his daughter/wife/sister?!" and that kind of rhetoric) instead of just
someone. Etc.
He was a misogynist, but he hated men as well. Basically I would say that from reading his manifesto, that he hated all of humanity. I think it's an oversimplification to say that misogyny was the cause of his actions. He killed more men than women in his spree, but even if that was not his intention it is clear that he despised successful men as much as he despised women. He wanted to kill both genders.
He despised men who had sex with women because they had what he didn't. He was jealous, not misandrist. He certainly was a racist though.