Google's John Mueller said a word I kind of dislike, "impossible." But technically it is true. He said, it would be impossible for Google to index the whole web. This was in response to why Google has not indexed all the pages in a sitemap for a specific web site.

Here is the exact tweet from John Mueller on Twitter:

Which issue do you mean, "indexed, not in sitemap" or like Martin mentioned, the opposite? We really don't index all pages in sitemaps or on the web, it would be impossible to do so. — 🍌 John 🍌 (@JohnMu) November 27, 2019

The issue is, new pages come up all the time. Sometimes those new pages are on purpose, sometimes not. Either way, Google cannot index every new page. In fact, Google doesn't want to index all the pages on the internet There are many stub pages, low quality pages, spammy pages and so on that Google rather not waste time crawling, rendering, indexing and ranking.

Google said impossible a couple of other times, first was when he said it is impossible to count links correctly on the web and the second was that it would be impossible to hand rank web pages in Google.

Forum discussion at Twitter.