Mass bends light because gravity warps spacetime itself, so light just follows the straightest path in that curved space. Mercury's wobbling orbit matched Einstein's math for this warping, while Newton's couldn't explain it.
But honestly, I first really got it not from equations but from watching a heavy football bend the net and a marble rolling around its edge. My tuition kid's textbook diagram of Mercury was just a cleaner version of that torn net.
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