A flat 4-4-2 isn't built for playing out: the two central midfielders get marked and the full-backs end up stuck. A few small rotations fix it. One central midfielder drops beside the centre-backs to make a back three, the full-back on that side pushes high, and the wide midfielder tucks inside into the pocket. Suddenly there's a free player at every height.
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They press with a front three. A flat 4-4-2 gets stuck, so we rotate.
Yes, with a couple of rotations. The flat shape makes it hard, so the team changes shape slightly when building.
Which central midfielder drops in a 4-4-2?
Usually the more defensive one, on the side where the ball is.
What if we keep losing the ball when we play out?
Expect it at first. Keep the shape, practise the same patterns in training under light pressure, and judge the decision rather than the result. If a game is getting away from you, it's fine to mix in a longer pass to the striker for a spell.