One of the reasons (besides the mentioned swelling) is that when you push, say, an arm through a gap, you are stretching skin and flesh (think pulling up a sock), which makes the limb thinner.
When you are pulling it out, skin and flesh crumples in the gap and makes the limb thicker.
To see it in an easier way: Wear a loose sock in your hand, and push it through a gap (for example between two couch pillows). Its stretches going it, but crumples when pulling out.
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