Asking my Professor to create a Google Account to submit a Letter of Recommendation for me

My best guess, and just a guess, is that he was frustrated with the system that was required, rather than with you. It is probably a mistake for any admissions system to require an email address from a particular provider (unless it was for a job at Google, I suppose).

I don't think you made an error, but if you want to ease the waters, go see him and apologize for the hassle of it all. It would probably be a mistake to just forget about it, but also a mistake to obsess over it.

Such systems infuriate me, also. Such extra accounts are always a security/privacy issue.

It is an unfortunate situation, and I think you misread it a bit. While your recommender didn't come right out and say it, when he emailed you to say that the submission site required a google account, it was a pretty clear message saying "the site requires a google account, and this is not acceptable to me".

You can assume that either he has an account and doesn't care to use it for this purpose, for some reason or other, or that he doesn't have an account and doesn't care to create one. Your correct next step would have been your last step -- to contact the organization and ask for an alternative.

I don't think it was some awful error. Like you have wounded the man.

I DO think in general that you should think about how people can help you and to make it convenient for them. And that what to you as the one who is benefiting (or as a possibly more tech savvy person) is normal may not be for them. Probably you should have asked the program ahead of asking the person how to handle people who did not want to create a login (and given the option ahead of time).

The only reason I am belaboring this is it is a bit of a general learning. Applies for customers in the business world, bosses approving expenses, etc. etc. The more you can make it easy in "hassle factor", the better. Make it easy for people to give you what you want! Maybe it shouldn't be this way and only the real big issues should be considered. But that's not how things work.