"A monopoly exists when a specific person or enterprise is the only supplier of a particular commodity" [0]. Bing exists so by definition, you are wrong.
For example, Article 102 of the Treaty on the Functioning:
Any abuse by one or more undertakings of a dominant position within the internal market or in a substantial part of it shall be prohibited as incompatible with the internal market in so far as it may affect trade between Member States. Such abuse may, in particular, consist in: (a) directly or indirectly imposing unfair purchase or selling prices or other unfair trading conditions; (b) limiting production, markets or technical development to the prejudice of consumers;
With Sherman Antitrust Act of 1890 we get supreme court cases that states things like: The purpose of the [Sherman] Act is not to protect businesses from the working of the market; it is to protect the public from the failure of the market. The law directs itself not against conduct which is competitive, even severely so, but against conduct which unfairly tends to destroy competition itself.
And in an other supreme court case:
The goal was to prevent restraints of free competition in business and commercial transactions which tended to restrict production, raise prices, or otherwise control the market to the detriment of purchasers or consumers of goods and services, all of which had come to be regarded as a special form of public injury. For that reason the phrase "restraint of trade," which, as will presently appear, had a well understood meaning in common law, was made the means of defining the activities prohibited.
Not a word about monopoly but a lot about behavior which in common speech people call monopoly but actually refer to behavior which is illegal according to anti-trust.
Whether you use anti-trust synonymously with the word monopoly doesn't change the fact that Google will still show Bing and Yandex in the search results.
An example of anti-competitive behavior here is actually from Amazon, when they had de-listed Apple TV and Chromecast from their marketplace for years because it competed with their Fire Stick.
Are you suggesting that we should ignore people misusing economic terms when discussing economic policy? I don't see how ignoring blatantly false facts is better than educating people such that they can properly discuss a topic using the proper terms.
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.
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.