Thought I’ve often had (but entry prompted by this one).

The distinction between sin and sinner becomes possible as soon as God says, “I’ll punish you later.  At that point your allowed to hope that something can be done about the punishment.  And you should want this to happen and be thankful for the time.

In other words, one reason we should love the sinner and hate the sin is because that is precisely what we are encouraging sinners to do.  They should love themselves enough to escape from their sins, which they should hate enough to seek rescue from them.