"Can anyone explain the logic behind the silent treatment?"
I can't tell you the logic behind it, but I can supply a possibility.
Many people today are just not capable of dealing with any type of conflict. For some reason the player may have developed some personal reason for not wanting to play with you or your group, and he(she) didn't have the courage to tell you about it. The "easy" way for this player to avoid direct conflict with you is to avoid talking to you about it, and hope you "get the message" or just lose the motivation to keep trying to contact them. The same type of conflict fearing folks are the people who break-up with a date by using the same avoidance tactic.
If you run into the player that has been dodging you, say at a game store, they will likely blame technology for not getting your messages, or say that their work schedule just overwhelmed them and they haven't been able to get back to you. If you pressure them face to face to attend a game session, they will probably use a work excuse to not be forced to tell you there is something about you or your game that they don't like.
To be clear, I don't condone this type of behavior. I have been a victim of the "conflict-phobe" myself, and it is incredibly frustrating. I have seen close friends of mine behave towards others in this way before, and when I asked them about it, they told me that they "didn't want to hurt the other persons feelings" by being frank with them.
I don't know how people become so afraid of conflict that they would prefer to actively avoid all communication with someone, but I believe it is the cause af many of these snubs.