Chunks glitch out with "bad" computers

What I expected to happen was...:
When I put on high chunks I should be able to see further

What actually happened was...:
When I put chunks on anything 8+, I start getting these chunk glitches (I think the world is loading the further chunks but are loading them closer to the player), and I can't play on higher chunks.
I have changing my texture packs to different ones, even the original one, but this bug still happens

Steps to Reproduce:
1. Get a computer that gets lag (40 frames max)
2. Change the render distance setting to something high (16 chunks)
3. And when you get back to the game, all these chunks start glitching out