I have for many years searched for answers myself. Like in the Matrix, I felt like something just wasn't right. That I was in a dream. Aside from all the B.S. you hear, here is the answer my friend. Einstein immediately, after his theory of SR., begin telling and explaining that the results, though mathematically precise, are OBSERVER EQUATED. In 1921 he wrote a book titled, Sidelights On Relativity. In this book he tried to explain that mathematical equations don't reflect the TRUE fact of a perceived view. Heck, he even admitted that he was wrong and he believed in the Ether. Not one took notice of the book, his theory was in full speed, and even he couldn't stop the farfetched minds that took his "idea" and started all the fairy tales.
OK, now some facts...
!) Einsteins second postulate, simply says, the speed of light is C in a single frame of reference. He didn't, wouldn't and never even meant to say that the speed of light in the same in ALL frames of reference.
2) Einstein himself later tried to explain that his theory is based on OBSERVER perceptions. He didn't think about all the crap that his idea would spawn. Namely, he never meant for his OBSERVER perceptions to be taken literally.
3) The fact is, Einsteins General Theory, was meant to REPLACE Special Theory. He realized the SR was a Pandora's Box of paradoxes, and quite frankly, wanted something more real, felt, and not just OBSERVED.
4) Mathematically, SR is flawless. The math is beautiful and does match up. But, still there even are paradoxes with the math. For one, if the traveling twin is REALLY, FACTUALLY, younger then the Earth twin, why doesn't anyone talk about how that younger twin is also skinnier (about as wide as a pencil), and ways 20,000 pounds!!! The math that dictates time dilation is real, is the EXACT math that also states that their mass will have increased, and their length will have shortened.
To sum it up, the world today has a vested interest in Special Relativity being the Gospel. But even within themselves, their not sure how to explain it.
That's why you get so many contradicting answers. To sum it up, look at the book "Sidelines On Relativity"  Einstein  1921, and visit the "Max Planck Institute For Gravitational Physics (Albert Einstein Institute) website. They themselves talk about Special Relativity and it's "perceived" only view.
Your intuitions are not wrong, and with it's many paradoxes and recant by Einstein himself, I would start studying General Relativity. GR makes sense, is mathematically sound, AND is not so counterintuitive as SR.


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