Do strict parents love their children?

In my opinion a parent should be firm and consistent. This doe not mean unreasonable. Strict is a term used when a minor is in disagreement with the parent.
My advice to a minor is to convince the parent that an action is need of change. Reasons for change are: time to make decisions for oneself because it is not dangerous, opportunity in a limited setting to make independent decisions when you have someone to fall back on, opportunity to prove ones worth as a logical thinker.
My advice to the parent is to remember that there is a fine balance between safety and over-protection. A child learns independent decision making skills a few steps at a time with trust that if a mistake is made that they can return to the parent.
Good luck and good communication makes for a good relationship.