“Mathematically, the twins’ paradox is proven to be impossible in real
life by the very mathematics.”


Nope.

Why is it a false statement? *The twins’ paradox presents this paradox
where each twin observes the other to be younger at the same time and same place.

Nope. That is NOT what SR says/implies.

SR implies that the inertial clock *you pose* as "staying home" will
indicate a greater value than the other one that rejoins it..
Depending on the narrated scenario, authors interpret/call this as
"aging". SR simply says tt' (and by how much). The rest is our
personal wordings that are not part of relativity.



*The said observed result
just can never happen in real life.

Liar. It has been done and observed.
It is done and observed on a regular basis.


Amazing garbage. *A paradox is a contradiction and cannot possibly
have been observed.

True. But you are confusing the two different meanings of "paradox".
(1) A paradox is an *apparent* contradiction.
(2) a paradox is a contradiction.

In the Twin "paradox", the word paradox has the first (1) meaning, not
the second one. You need to learn the meaning of the words used in our
community if you want to understand us.