If you chase their hand, then you are removing your own guard... opening the door for him, in order to try to get his hand. This is why those standing wrist locks are so hard to get on people, out side of the dojo. You are busy chasing his hand with yours, while he is busy punching you in the head. You can't block with the hand you are chasing his hand with.
I like to punch him in the head. If I punch him in the head... great. If he blocks, or covers up... I make contact with his hand or arm. Now, I can control where his hands go. Boxers do this all the time. In order to open the head, for a head punch, they punch the body. The other gets tries to stop the body punches and lowers his guard, opening the door to the head.
If you start chasing the hand, to pull it down, you are essentially going for that standing wrist lock. You are lowering your guard, in order to try to catch his hand. He didn't even have to work your body, you just opened the door. Also, you will now be more likely to fall for his feint. He feints his hand one way, you got hit last time you didn't catch it, so you try harder this time to catch his hand... you end up opening your guard even more.
In order to make that standing wrist lock work... punch him in the head. (if you KO him, the wrist lock is much easier to get

) When he blocks, he puts his hand or arm into contact with yours. You don't have to chase it at all. So, punch him in the head until he starts to block it. Now, you know his hand will block it, maintain the contact between your punching hand and his blocking hand. Now you have a decent chance of pulling it out of the way, or finding your wrist lock. The key is you did not chase his hand, he gave it to you to block your punch. As long as you maintain the contact, you each still have only one free arm.
The other advantage here is that he is reacting to you. His first concern is not getting hit. This gives you the time to pull or apply the lock. The pull will be a higher percentage move than the lock... getting a lock in this set up, is much more possible than catching the hand out of the air.