There is no right to be forgotten, because it would mean I don't have a right to remember and thus share that memory.
That's not what the right to be forgotten is. It would more accurately be described as the "right to be forgotten by commercial entities".
In the EU we have data protection laws that affect anyone collecting personal data for business use. For example a company with a client database must take steps to ensure that it is protected and people's personal data is not leaked, and that it isn't sold for profit without consent. There are rules concerning things like credit reference agencies keeping data on things beyond the period which they can legally be considered, e.g. bankruptcy that doesn't have to be declared after 5 years. Subjects can also request that their data is removed if they no longer have any relationship with the company, e.g. if you close your Facebook account they must remove all your old data too.
In this case Google crawls the web for information about people. They must treat that information according to data protection rules. It doesn't matter if the information is a matter of public record. An old bankruptcy might have been written about in a newspaper, but that doesn't mean that a credit reference agency can report it after 5 years. People may remember, they may not, that's just life and a measure of how noteworthy the individual is. The point is that when they apply for a new business loan the credit reference agency isn't allowed to remind the bank. Even if the bank employee remembers they can't use that information in their decision, and if they do they won't be able to justify it to the regulator later since the credit report didn't mention it.
People use Google to research other people. Google is extremely good at finding and sorting information about people. Why should Google be allowed to opt out of rules that affect credit reference agencies, for example?
Note that your personal right to remember is completely unaffected. You are not required to forgot or remove information from your personal web site.