With Greeks able to easily move to other countries, why is Greece's unemployment rate so high?

Greece's unemployment rate is 24.4%.  People can easily move to other countries within the EU for jobs.  So why don't they?  Could it be unemployment insurance benefits?  But people are only eligible for the benefits if they have already held a job and paid into the insurance system.  One would then think that the unemployment rate among older people would be high relative to that for younger ones, but the unemployment rate for young Greeks is 51.1%.  The ability to move should also be easier for younger people so that would also work to lower their unemployment rate.

Another possibility is that Greece just has high general levels of welfare benefits.  Greece recently went so far as wanting to classify paedophiles, compulsive gamblers, fetishists, exhibitionists and sado-masochists, and pyromaniacs as eligible for disability benefits.

First, Greece launched a large scale welfare upgrading, including an expansion of social insurance coverage and an increased access to health care in the 1980s.
While government revenue is approximately 37 per cent of GDP, the over-committed social welfare benefits have pushed up public current expenditure to nearly 90 per cent of its total revenue, leaving only a small remaining portion for interest payments and investment. . . .

From Bloomberg:

Clearly, the welfare-state expansion in Greece and Portugal was part of the reason these two countries ended up as clients of Europe’s bailout mechanisms. . . . Yet surprisingly few people in Europe have bothered to understand the role that the welfare state played in creating it.  . . . . State spending in Spain will have to shrink by at least a quarter; Greece should count itself lucky if the cut is less than a half of the pre-crisis expenditure level.  The worse news is that this is likely to be only the first round of welfare-state corrections. The next decade will usher Europe into the age of aging, when inevitably the cost of pensions will rise and providing health care for the elderly will be an even bigger cost driver. . . .

Robert Samuelson:

The threat to the euro bloc ultimately stems from an overcommitted welfare state. Greece's situation is so difficult because a low birth rate and rapidly graying population automatically increase old-age assistance even as the government tries to cut its spending. At issue is the viability of its present welfare state.

The main discussion in these articles are the extremely generous pension benefits that allow people to retire in their early 50s.  Yet, that won't explain why young Greeks won't move to other countries to look for work.  It would be nice to get detailed data in English of Greece government spending.  If someone has this, I would find it very helpful.

The New York Times described the necessary spending cuts as "the dismantling of a middle-class welfare state in real time."

A comparison of overall to youth unemployment rates is available here.