Misogyny: hatred of women. (from Greek: misos 'hatred' and gunē 'woman'). 
Feminism: the advocacy of women's rights on the grounds of sexual equality. 
If there's one thing most people in discussions in the media, online and off-line are very assured about, then it has to be their conviction that their definition of specific terms have to be the right and precise ones. This is why some of the most abused terms whenever it's about men and women (or when people think it's about this subject) are those of feminism and misogyny, as well as their derivations. The awkward part about these fiery displays of self-assurance is that there's a painful absence of a clear definition of these terms both sides like to wield so prodigiously.
Let's start with the easy one: misogyny. Seems straight-forward enough, doesn't it? Someone hates women in general, ergo said person is a misogynist. Yet the problems arise when one starts asking what it is that this person hates and what defines women in such a sense that they are all included in this. Take for example the person most recently called out as a horrible misogynist: Elliot Rodger, the shooter in the 2014 Isla Vista, California shooting which killed 8 including himself. 
What did Elliot hate? Did he hate all women? No, to one reading his autobiography it becomes quite clear that he is only interested in - or rather obsessed by - the blonde, Caucasian type girl. What he hated was that they didn't flock to him. Over time this sense of rejection grew into hatred. In his view blonde, Caucasian women became 'women' in general. He didn't hate fat or ugly girls, he just longed to have this one perfect girlfriend. Unable to fill in this pre-formatted space in his head with a girl fitting the description, his obsession culminated in rage as he never found himself able to reflect upon this urge and deal with it.
Since 'blonde, attractive, Caucasian' women isn't 'all women', Elliot wasn't a misogynist. Just someone who was raised in an environment which apparently promoted the growth of pre-existing tendencies. The autobiography brings forward the image of an introverted individual who is convinced that he is extroverted, a dangerous situation for one's psyche because of the high probability of disappointment. In the end he found solace among others who blamed their problems on 'women', yet always in the most generic terms possible. No one hates women in general. No one can define exactly what they hate about 'women' without getting stuck in generic descriptions which would fit many men as well.
Much of the issue here is that of defining what a 'man' and a 'woman' are. What makes one into one and not the other? Do we truly have two distinct groups? What is 'masculinity' and what is 'femininity'? As someone who is both and yet neither due to being born in an intersex body, many of such related questions have been asked of me. Despite spending so many hours thinking about how I would define myself, or rather what parts of my personality could be defined as either feminine or masculine I can still only conclude that they're irrational stereotypes without a solid founding in reality.
Would a misogynistic person hate only, say, fifty percent of a person like me? Only the feminine bits, essentially. What if these properties are also found in men? When it comes down to it all properties can be assigned in relatively equal amounts to both men and women, whether it comes to patience, management capability and not getting lost. The only significant differences can be found in the brains, where brains defined as 'male' have a more pass-through structure, whereas 'female' brains are significantly more interconnected and are more aimed at analytical processing instead of snap-judgement. These are just the two ends of a spectrum, of course. From these tops at either side a gradual merging occurs until both types meet up in the middle.
Fine, you may think at this point, but if misogyny is - if you'll excuse me - a bit of a misnomer, then surely feminism is quite undeniable and easy to understand, right? In a way, yes. In Western society the group of individuals classified as 'women' based on their biological sex have for a long time been considered to be inferior to men for rather shaky and unscientific reasons. The reversal of this process and the harmonization of society into a more merit-based one has to be seen as one of the biggest sociological accomplishments of the 19th and 20th century which continues to this day. Yet when the easy to grasp part was done and over with and all women had the right to vote, the right to marry who they wanted, decide when they would get pregnant and the many stigmas surrounding women in Western society began to fade at long last, the nit-picking started.
The part where things go bad here is that at some point feminism crossed from the territory of 'suppressed group of individuals' to 'women's rights'. While some of the current issues at stake are fair ones, such as equal wage and everything else that fits into a merit-based system, things get fuzzy quickly when it zips into issues such as 'representation'. Why would any group of people in any function have to consist out of roughly half men and half women? What is the rational explanation for this? It's obviously not merit-based, but instead seems to make the assumption that 'it's the right thing'. While equal representation is logical in politics, in many other areas it's a curious position at best.
Here too starts the issue of trying to define 'women' and 'men'. Women are better at A, because of specific reasons, as well as at B and C. Yet 'women' isn't 'all women'. While some women are great organizers, or skilled with various technologies and the like, you see a similar diversity as on the male side of the spectrum, with those who can do marvelous things with a piece of wood, a computer or who are great leaders, while a similar number would be helpless at any of these tasks.
Ironically the insistence by certain individuals who call themselves feminists on various topics usually lead to blanket statements made about 'men'. Listening to some of the ranting done by these prominent figures show a disgruntlement towards men more severe than what even Elliot Rodger raged about in his autobiography. If anything these so-called feminists went straight from feminism into the exact opposite form of misogyny, missing of course the point that this straw man they set up of 'men' is largely fictional. The diversity of personalities among the individuals marked with a biological male sex is such that it is impossible to classify them all as part of one singular group.
This is something which I as an intersex individual understand quite well, as 'intersex' is the very definition of diversity. It covers thousands of medical conditions and biological variations, with each individual different from the other. I am an intersex individual, but I'm not every intersex individual. In fact I would say that I have very little in common with most intersex individuals, both physically and in terms of personality. This is no different from the diversity among so-called 'men' and 'women'. It's this diversity which makes all of us so very different and yet so very much the same.
 Concise Oxford English Dictionary, 12th edition.