On the animation looks like the Motor wants to spin but the linear shaft is blocked. I would uninstall the shaft and see if the motor turns then
EDIT: Also make sure it turns in the write direction
Is your z axis carriage definitely horizontally parallel with the print bed as I had the same issue and after a bit of calibration and lubricating the threaded rods it was fine and now prints with amazing quality
I have an Anet A8 too. Your problem might be backlash due to the fact that the parts provided in the Anet A8 don’t have tight tolerances.
To temporarily solve the problem, unlock your steppers, turn your Z-axes by hand to level them with a ruler. Make sure the Metal threaded nuts attached to the X-axis plastic parts are exactly the same height above the acrylic plates that your Z motors are mounted to.
If you re-do this process often, this should allow you to print correctly.
To permanently eliminate backlash, use the item from link below (or one like it, you can print one too if you have a spring, search “backlash” on thingiverse) and do the above process.
I think tomwaltera gave you the good answer. Anyway chech the polarity. Anet a6-8 z leveling is a pain, it always get unleveled even with antibackslash
I have the same problem. No matter how I try to level the z-axis it goes off when I “home” it.
It seems my threaded rod is off-plum and will not stay parallel with the guide rod. I lashed them together near the top with a zip tie and that has helped, but does not seem like a good permanent solution.
A recommendation for you: Anet A8 Motor Mount Replacement (with Z Axis REAL Fix) by klownius - Thingiverse 145
why not use this instead? Anet A8 Z-axis support by Autro - Thingiverse 45
or this? Anti Z Wobble for Anet A8 by saschai - Thingiverse 15