Let's say the character has over the years grown to dislike humans because he had many negative experiences with them, and is disappointed in humanity itself. How does one write such a character without making him too edgy or unlikeable?
Often what makes a misanthropic character likable to the audience is their sympathetic behavior or expertise in worldly matters. If the structure of your story does not have the time for (or does not aesthetically permit) that the misanthrope in question have an extensive backstory in which their lost hope, shattered dreams, and gradual metamorphosis into misanthrope is conveyed, then a good alternative might be to show how their misanthropy informs their expertise, and allows them to deal with the world in a more realistic and savvy way than other characters, who are are still weighed down by their sentimentality towards humanity.
Dr. House comes to mind. His misanthropy often makes him a better doctor, at the expense of his human relationships. It is hyperbole and might not translate into real life, but mental instability in exchange for heightened technical ability is a very old trope. It can be downplayed, played straight, or exaggerated.
Downplayed: An unsociable, grumpy man is a good car mechanic due to his extensive time alone.
Exaggerated: A sociopath's complete detachment from humanity, lack of empathy, and talent for manipulating the emotions of others make him the perfect political candidate.
You'll find a lot of good answers here: How do you make a story succeed in spite of an unsympathetic main character?
On top of that: If your character is a misanthrope out of disappointment, that's your hook. Disappointment means that the person once had hope. So you play on that past hope.
Was he an optimist? A starry-eyed idealist? A romantic? A decent man who was taken advantage of? An ordinary bloke in an abusive relationship? A middle manager keeping his head down who watched fellow citizens vote a tyrant into power?
Figure out what broke his heart. Find a way to convey that backstory to your audience (not immediately — somewhere between one-third and two-thirds of the way). A cabbagehead, newbie, or Watson are some traditional vehicles for this kind of exposition; you can also do it via a third character or a flashback.
Additionally, if he can retain some of that hope, even in flashes (think the grouch with a heart of gold), the reader can see that the misanthropy was situational, or earned, and that there's some good underneath which just needs uncovering.
A likeable misanthropic character is not necessarily a misanthrope at heart: he only needs to act like one. He is misunderstood. Perhaps just different. They could even be a good character who turned sour as a reaction to a bad break, and you could add a growth/redemption arc, in which to play this reveal.
Some great misanthrope characters in TV and literature are: House MD, Sherlock Holmes, Ebenezer Scrooge. All these characters are perceived as misanthropic, but their story arcs reveals that, in truth, they are not.