The twin paradox isn't a really a paradox. It becomes a paradox when you visualise it incorrectly. The many explanations on YouTube could be misleading in this context. I have seen some videos where it tries to explain it's the acceleration and the deceleration causes it - obviously wrong. Some do say that since acceleration is involved you need GTR (General Theory of Relativity) to explain - wrong again.
The twin paradox can be explained using the STR (Special Theory of Relativity)
It's hard for me to explain or present everything here.
Paul Davies in his book "About Time" had an excellent write up and also there was a translated Russian Book about Relativity - I forget the Author but it also had a decent explanation. The Russian book was aimed at the layman and hence it did not involve much mathematics.
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