I know this is a joke, but i think the idea is that you would only look stretched to outside observers, but you yourself actually wouldnt perceive any stretching going on.
I think you literally stretch; the part of you that touches the horizon line first experiences infinite gravity, while the parts of you outside the horizon line don’t, so you’re getting stretched out as the parts inside the horizon line fall in much faster
Edit: read the reply to my comment, they’re probably more right than me lol
If you fall into a black hole, you can do no experiment to detect the horizon, it’s a completely unremarkable region of space to you. Infinite gravity is only really a thing at the singularity, but that’s almost definitely just because our theoretical models breakdown and stop giving accurate descriptions of reality there.
The stretching is just because of tidal forces, which means that gravity gets so much stronger closer to the black hole that your feet are pulled harder than your head, you experience the same thing standing on earth, it’s just that the change in gravity is basically negligible here.
Source: Was a black hole physicist for a while
Small edit: Tidal forces stretch you in the exact same way that they stretch the ocean, thus creating ocean tides.
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