Sometimes when cuttings are rooted in 16oz or 32oz clear plastic pots and are being transferred to bigger pots for summer, the roots stuck to the walls of the clear plastic pots are broken and remain stuck to the original pot. I tried a good pre-soaking in water but helped only marginally. Any other suggestion?
It does not happen when the roots are weak.

If you are using cups that are not rigid, you can squeeze them to get the roots to pull away, or squeeze and then let them "snap" back, and the roots will be shaken loose. Sometimes you have to repeat a few times. If the cup cracks, so what. They are cheap, and they can be used again even if cracked - they don't have to hold water.

Very occasionally, I have to use something pointy to tease a root off of the wall of the cup.