If Google were to try and charge users for search, everyone would immediately switch to bing which keeps them in check from raising prices like they would if they were the only provider of search. They are in no way a monopoly.
If you substitute "harmfully disproportionate market power" for "monopoly", the points most people are making remain similar.
> educating people such that they can properly discuss a topic using the proper terms
Where did you do that? The only recommendation for a better term I see is "harmfully disproportionate market power", still quite a usable mouthful and made by someone else. Your contribution seems to boil down to "your wrong", and I'm still unsure if this is intended to be about the use of the word or the actual point. Probably both, with one being secretly used to support the other.
Google -> search results (for free) -> website (owner paid for seo/adwords and charge the customer)
Similar thing happened with google maps while they were never a monopoly by your definition because other solutions exist.
But as site owner, you need traffic. SEO for some search engine built by your brother, used exclusively by your family, wont help you grow your business. You need eyeballs, and more than 90% of those are on google [0]. Pretending this is a perfectly functioning market and websites can just ignore google is... unrealistic.
[0] http://gs.statcounter.com/search-engine-market-share