The reason to take the time to harden off seed-grown plants is the same reason you would protect your "winter legs" from getting sunburned at the beginning of the summer. They have to be acclimated and protected from the stronger UV rays.
The stronger outside light can cause sun scale to the plant cells and possibly death.
There are many seed and plant websites with videos and detailed guidelines, but here are the basics:
Positively Pennsylvania
Pennsylvania Farm Bureau March/April 2018 Vol.11 No.2