Actually,it's quite simple.
All dogs,regardless of breed,have predatory instincts passed down from their ancestors.And depending on what breed,or breed mix you have,the instincts may be stronger [such as with hunting breeds,or guarding breeds].
It's not the kid on the bike they're after,it's the whole moving object. And once the object stops moving,they lose interest in the chase. This is a behavior that you want to modify though,since it could lead to injury for your dog,or whatever it's chasing. Even if your dog's safely behind a fence,they can still cause harm to themselves by biting the fencing,or struggling against the leash. And trust me,you don't want your dog to ever catch a moving tire of anykind,it could kill them.
There is also a territorial instinct that plays into chasing behavior,but usually more of a minor role.
Territoriality can be a BIG problem if it's being focused on anyone or anything else who lives,or visits that particular dogs home.
The easiest way to correct this problem is to never let it start. Let your dog know from day one that this is your house,your yard,and everything in it [including his/her food bowls and bed] is yours. [This is NOT being rude,selfish,or bullying as far as your dog is concerned.] The point is,if your dog feels a need to guard or protect things without being properly trained to,this is a dangerous behavior. And it should be modified.
If you want your dog to help protect it's home,that's great! But get a professional trainer to teach you how to train your dog to do this job right.
[With Flash,he's been trained to watch the front door from the time it's knocked on,until I give him the signal to relax,this way he gets to protect his "pack",and do it safely for both him and our visitors.]
Sheba's my alarm dog. If there's a vehicle that pulls up into our driveway,or a knock on our door,she barks to let me know someone's here. And if it's someone she doesn't recognize [or trust] she has a special bark that she does,to alert me to strangers,or danger.
I do not suggest that you try to train or modify any of your pet's behavior though until you've atleast consulted a professional,that's what they're trained for. [And any reputable trainers will give you a free consultation,possibly in your home.]
Jayde-Packleader,Ron-Alpha Male,Richard & Rodney-Troublemaking Toddlers,Sheba & Flash-My Best Fur Friends