My constant debate with athletes and coaches is HOW MUCH speed and agility can be created; how much is genetic, how much can be manufactured?
I can tell you this; for sure you can increase these skills through training. One of my favorite drills is the side step and plant with hurdles. Moving laterally down a row of hurdles back and forth by planting on your forefoot, stay stable and fluid. Move your arms in your typical running form type action (see drill above).
Try this drill starting first to your right, then to your left. Practice this regularly, then see how much speed and agility you can create!