> At what point does one's right to be forgotten supersede another's right to remember?
>
> If Alice knows something about Bob because of their personal interactions, as he asks her to forget about it, but she still remembers it, is she violating Bob's right to be forgotten?
>
> etc.
No, no-one can force you legally to forget something, and I think this brings up the main problem with your argument, which is that we're not talking about Alice and Bob, we're talking about Alice and Bob's Widgets INC.
I'm technically minded and I see a 100% separation between the interaction between Alice and Bob, and Alice and Bob's Widgets INC. Yes, I do think it's completely reasonable for Alice to ask bob to be removed from log files, journals whatever.
Lets look at a parallel you drew:
> More concretely, suppose Bob visits Alice's house, and then a couple of weeks later tells Alice that she must forget that he visited. If she ignores his request is she violating Bob's rights?
I wouldn't say that Alice is violating anyone's rights here. Being unreasonable, yes. Asking for something with no legal or enforceable basis, yes.
> Now suppose Bob is visiting Alice's website, which records his IP address in a log file. Bob asks to be removed from the log, and again Alice ignores his request.
This is a non sequitur, these are different scenarios with different requests, just with the names kept the same. Businesses aren't people, and they don't have memories like people. Businesses don't (for the most part, legal actions notwithstanding) need IP address information. It can be helpful, certainly. Knowing your customer has returned, knowing what they have looked at etc., but it's not essential.
So yes, it's reasonable to ask for removal from logs, and no, it isn't reasonable to ask someone to forget you visited their house.