According to John Mueller from Google, mobile friendliness is not equivalent to mobile-first indexing. In order to move a website for mobile first index, diverse kinds of things are considered by Google and it is definitely beyond whether the website is optimized for the mobile devices or not.
On the occasion, a site can be designed with mobile friendly feature. However, it still may not be considered for mobile-first indexing by Google. It may not fulfill certain other criteria.
Giving some guidance to reply on a thread on Reddit that says,
“Despite being mobile friendly, what could be the reasons for Google to use a desktop crawler as a primary crawler?”
Different crawlers are generally used by Google based on the regular index or mobile-first index.
Through the Search Console, the site owner can easily know whether Google has used desktop or mobile version of the Googlebot for crawling the site.
Now-a-days, most of the websites are designed for the mobile-first indexing. Therefore, it is quite natural to expect mobile version Googlebot while looking through Google Console reports.
In case the site has been crawled by the desktop Googlebot then it quite naturally means that the site has not been moved to mobile-first indexing for some reason.
So, the question is why the site has not managed to get mobile-first indexing
John Mueller regarding mobile-first indexing
One of the most important criteria to move a website to a mobile first indexing is identical content for every device on every platform. If there is content in desktop version that cannot be seen through the mobile version then it may not be considered for the mobile-first indexing.
Mueller has said that there is no reason to worry if important content is shown on all devices.
Following to a hard scrutiny by Google algorithm, the site may not be given mobile first indexing due to minor discrepancies.
In Reddit, Mueller has said
“That said, if you’re sure that the content is all there on mobile, I wouldn’t sweat it. Sometimes out algorithms are a bit on the conservative side in that regard. A variation I saw a few times was that our algorithms were holding back a site because it didn’t have the same number of related items linked on the bottom of a product-page / post — yes, that’s a content difference, but you probably don’t need to care about it because it’s not going to change how your site overall is showing in search.”
Some differences may be noticed if one of the items may be missing from one of the versions of website. It can be structured data, internal links, images or something else.
“Obviously, it could also be because your site has real differences, like missing structured data, fewer significant images, bad internal linking on mobile, etc — these are things that those who don’t look deeply might miss.”
In case you have trying to achieve mobile-first indexing and not managed to get it then you must look at the content parity.