Why is Kaer Morhen in such a bad shape?

Kaer Morhen was attacked by the neighboring villages many years before. This theme (of Witchers being distrusted and "unnecessary") is explored throughout the game

If I remember correctly, ideas that the Witchers are not required due to the falling demand for their services are also shown.

I do not believe the actual attack on Kaer Morhen is shown in any of the books or games (may be wrong), however there are some logs of the time of the attack itself during the first set of Wolf School gear scavenger quests.

"In older times, witchers trained and underwent mutations here, but years ago a horde of fanatics, their hatred incited by various publications defamatory to witchers, such as the Monstrum, laid siege to Kaer Morhen. The mob could not have captured the fortress nor later laid it to ruin without the help of mages.

The attackers killed every witcher or witcher in training within, except for Vesemir. This was not the complete (or nearly complete) end however for the witchers of Kaer Morhen; a handful of them were out on their paths during the time of the attack, thus surviving. Currently only Vesemir actually lives in the keep for most of the year, although some other witchers (including Geralt of Rivia) sometimes rest here between their assignments, often during the winter" http://witcher.wikia.com/wiki/Kaer_Morhen

I highly recommend playing both, Witcher 1 and Witcher 2. If you enjoyed TW3 and would like to know more and experience some great RPG's, you cannot go wrong with either game. If you like to read, yearn for even more insight, I highly recommend checking out the Witcher saga novels. They are absolutely fantastic.

Well if I'm not mistaken, there were 23 senior witchers/professors and 40 pupils at the time of the siege of Kaer Morhen. Some witchers were on the path (Geralt, Eskell and Lambert being some of them) so weren't in the fortress. They had also the mage who was responsible for the supervision of the trials of the witchers. Vesemir was a fencing teacher and the only one that was in the fortress to survive.

Don't know how peasants killed that many witchers, but it might have been by the sheer might of numbers. The mages helped and probably most of the senior witchers were trying to protect the younglings.

(This was what I gathered from various forums, wikis and my own speculation too if that matters to anyone anyway).

Kaer morhen was attacked by a sorceress whom controlled monsters, she had convinced the king that witchers was unnecessary due to the lack of monsters these days but she had ulterior motives, a Witcher had killed her mother or something and wanted Revenge.

So the fight was made up of about 40 witchers counting both kids and adults versus a horde of monsters, peasants with pitchforks and a sorceress, only survivors was Vesemir and the 4 Witchers you now see or read about in the game/books.

Geralt was only a new recruit at the time and had probably just passed his trials by the time of the attack, Vesemir was about 60-70 when this happened, that means geralt would've been about ten years old.

Spoiler: if you watch Netflix's "The Witcher: Nightmare of the Wolf". During Vesemir's prime age, Kaer Morhen used to be a school of witchers.

There were fewer and fewer monsters. The Mages, masters of mutagenic alchemy ( potion for trial of the grasses ), at Kaer Mohren started to create crossbreed monsters. More monsters mean more business for Witchers. Humans respect witchers for killing monsters.

A sorceress Tetra, whose mother was killed by a con witcher, revealed to the people that witchers were creating monsters. A group of soceresses, local peasants and Kitsu, a powerful mutant Elf and Mahr crossbreed attacked Kaer Mohren.

Only Vesemir and a group of boys apprentice (including Geralt) survived.

I dont know alot about Witcher. but I know Kaer Morhen was feared and hated by most because of the witchers training there. as this Wiki link states. It was under siege Monstrum and also mages. Hope this answers your question.