Britain is considered to be mature Democracy and expert in solving International problems.Why then it is in muddle over BREXIT decision?

The only people in a muddle are the actual MPs, because far too many of them think we voted the wrong way and are trying to stop it.  So there is a majority of MPs who want to ignore a democratic vote.

The actual government wants to make Brexit happen but at the last general election, it didn't win an overall majority of MPs, so it couldn't be sure of getting anything done.  Now what would normally have been done in the past is for the Prime Minister to ask the Queen for another general election, and that normally solved the problem.  Unfortunately  the minority partner in the 2010-15 coalition insisted on passing a law that prevented this without a 2/3 majority in the House of Commons voting for it - the Fixed-term Parliaments Act 2011.  This totally screwed everything up.

However, there is always a way!  What Boris Johnson did was introduce a very short Bill to say that there will be a general election on 12 December 2019, that only needs a simple majority of MPs to vote for it, they did, so there will be a general election.  With any luck, this will produce a Conservative majority government and Brexit will finally get DONE!  Opinion polls at the moment suggest this will happen.

Because it’s breaking out of the new world order

The Left in Britain is really pushing for a Globalist agenda. The EU is full of people like that. The Left in the West wants a decline of nationalism, similar to the United States. They need to reinvent how people identify as British, and the resistance is from those who don't want to give it up. Globalism is a terrible thing.