But Trills, the dictionary does also explain that misandry is a neologism, and misogyny is a word with a long history, and the two have different applications.
If you look in a sufficiently basic dictionary, you can find words defined with great simplicity. That does not mean that it's incorrect to point out that these two words do have more precise meanings and connotations.
Take the word 'utopia'. Most people nowadays would associate the term with a perfect place, or an idealized world. The etymology, obviously, is 'nowhere'. The dictionary would get into all the historical layers of meaning built up from Thomas More onwards.
Then take the term 'dystopia'. It's a relative neologism, though the time difference is much less than that between 'misogyny' and 'misandry'. The etymology is just as clearly rooted in Ancient Greek, and just as simple to state. The meaning 'a bad place' is quite simple too. But if you looked up the word, and if you thought about it, you'd find it very hard to understand the term without the cultural freight of the pre-existing term 'utopia'. Because the second word is piggybacking on the first.
If you wanted to say simple 'duh, bad places exist in the UK so the UK must be a dystopian society', you'd be correct insofar as your statement recognizes the most basic etymological content of the term. But you'd also be judged incorrect by anyone who understood how the one term as derived artificially from the other.
'Misandry' is derived from 'misogyny' for political reasons, by people who would like you to think that everything is so equal, women hate men just as men hate women. But if you understand the history of 'misogyny' as a term and of 'misandry' as a term, you can't simply go to the etymology or to the 'dictionary definition' in isolation and expect to make sense. IMO.
(No idea if that clarifies or not, if not I'm sorry.)