What are the reasons for leaving the EU?

I am assuming that you are referring to the reasons that many people in the UK gave for voting to leave the European Union on June 23, 2016, a.k.a. Brexit. If not, we can still look at Brexit as a case example of why any country might want to withdraw from the European Union.
There were a number of reasons UK citizens gave for voting to leave. The most common one was a desire to limit immigration into the UK. Over the last decade or so, millions of people immigrated to the United Kingdom under the freedom of movement allowances that membership in the EU allows. Those who felt that too many immigrants from other EU nations were coming into the UK unchecked tended to vote to leave the European Union so that their country could institute its own controls over who gets to cross its borders.
A desire to stop paying membership fees to the EU is another reason why some might want to withdraw from the EU. The UK paid £13.1 billion to the EU in 2016 alone. Some saw this as a large and disproportional payment of a nation's capital when smaller nations pay much less.
The ability to control its own imports and exports is another often cited reason for withdrawal from the European Union. The EU is a large "single-market," and trade within the EU does not incur any tariffs. Some feel that by withdrawing from this market, a nation would be better able to take control of trade so as to specifically benefit itself. It should be noted that many economists see little validity in this argument.
A less tangible, but still important argument has to do with the issue of national sovereignty. Being a member of the European Union means that a certain degree of the decisions that affect a country are made by people of other nationalities. Many nationalists feel that withdrawing from the EU means taking back control of their country's affairs.
https://www.economist.com/books-and-arts/2017/04/29/explaining-britains-vote-to-leave-the-eu

https://www.theweek.co.uk/brexit-0