A few reasons:
Hebron, a city in Palestine, was recently recognized against heavy Israeli protest as a world heritage site. This was the turning point that brought us to where we are now.
Additionally Unesco is voting a new chief in. Current leaders are Hamad bin Abdulaziz al-Kawari (Qatar) and Moushira Khattab (Egypt), along with a French national Audrey Azoulay. Israel knows the next leader isn't going to be pro-Israel and likely side with the 'anti-Israel' rulings.
Second big reason is America's push to isolationism. America has been withdrawing from its seat as a world leader in several capacities under the Trump administration, including the Paris Accords, NAFTA, and anything else they can get their populace frenzied about. Something you can see from a few world leaders' statements:
French UN diplomat: "“part of America’s DNA” and that “we need an America that stays committed to world affairs.”"
And Russia: "“one of the countries that founded the UN system” is “a shock and a pity.”"
UNESCO is a growing financial liability to some degree and separating from it for financial reasons is also a likely reason for this move.
Info on Hebron:
Trying this for a second time. "UN designates Hebron tomb revered within Jewish faith as Palestinian heritage site" is the headline ran by the independent here http://www.independent.co.uk/news/world/middle-east/hebron-tomb-palestinian-heritage-site-un-jewish-faith-ibrahimi-mosque-jerusalem-a7829261.html
Hebron contains multiple religious sites, the two major ones in conflict here is the Muslim site of the ibrahimi-mosque and the Jewish site of the Tomb of the Patriarchs. It also fully lies in a 'disputed zone' where Israel claims it as theirs while UNESCO continually gives Palestine authority the nod there.
As much as the Jewish claim being ignored, the major issue presented by Israel has more to do with one particular wording by UNESCO. from here https://www.standard.co.uk/news/world/donald-trump-quitting-unesco-sends-a-warning-to-other-un-bodies-over-palestine-london-expert-warns-a3657426.html "“What’s most angering Israel is the labelling of sites in East Jerusalem as on ‘occupied Palestinian territory.’""
UNESCO of recent has been accused of having a Muslim majority ruling it and have been making decisions that are being called skewed as pro-muslim and anti-hebrew. Referring to Palestine sites as 'occupied' (IE belongs to Palestine but occupied by Israel) is heavily contentious.
Its also interesting to note that the worldjewishcongress is heavily advertising this, pumping a good chunk of change into google adwords to ensure their viewpoint is readily seen. Edit as per comment : Typing in "Hebron UNESCO Israel" into google gives the first result with a little 'ad' symbol beside it as https://www.googleadservices.com/pagead/aclk?sa=L&ai=DChcSEwj9ycLjl-7WAhWPPYEKHT8SD54YABAAGgJ5dw&ohost=www.google.ca&cid=CAESEeD2HYgUQmeAbTU-tJnyBrOq&sig=AOD64_071ndha_5bMKaBqZgQZ_6YZytvZQ&q=&ved=0ahUKEwit0brjl-7WAhXhlVQKHbx_CiYQ0QwIJg&adurl= Google keyword advertising may differ pending your location.