Although similar questions have been asked before (such as this one), I would like a bit more background information on why answers are deleted from a user's page when a question is migrated to another site. I can understand why the question itself is removed, but I would feel cheated if I put a lot of thought and effort into an answer only to have it vanish entirely from my user page. Furthermore, even if the question itself is off-topic for Stack Overflow, I may still want to refer back to it and my answer at some point in the future. Is there some technical or philosophical reason why this information is completely removed from user pages?
It's removed on your user page on the original site, but it will appear on your user page (if you have one) on the destination site.
If you don't have an account on the destination site, you should be able to make one and then the post will either be automatically linked to your new profile or you can email firstname.lastname@example.org to link it for you.
When a question is migrated, that means the question didn't belong on the source site in the first place.
Therefore, there's no reason to keep track of the answers on the source site either.
If you have an associated account on the target site, any migrated post will be auto-associated with that account. So the posts don't disappear, they just get moved to where they belong. (If you don't have an account on the target site, if you create one and associate it, the new account will automatically take ownership of the posts.)