Google are not against AI, at all. In fact, they are entirely the opposite - huge advocates of AI, and to a very real extent, have done more to bring us to the point of current AI than anyone else. Google invested extremely heavily into AI and robotics many years back, hiring a lot of the absolute brightest talent, and have published research papers and code both, used heavily by others, and that most especially includes OpenAI.
Google itself uses several different AIs in various parts of its systems and operations. On the search side, they started using Machine Learning for their search results well over a decade ago, introduced an AI called RankBrain that helps serve the right results based on user intent, have an AI called SpamBrain for filtering out a lot of spam (including low quality, machine-generated spam), developed Language Models and Transformers, such as BERT and MUM etc.
They are big, big fans of AI.
However, they are very much against low-quality, built to rank, spam that adds no new information to the search index. Their search index is magnitudes larger than the knowledge of ChatGPT, so anything ChatGPT has learned from its index, the corpus of training documents, is absolutely certain to be data that Google have already indexed.
If you use ChatGPT to merely rearrange information that is widely known to create a page that will pass plagiarism checks, and yet still be 100% derivative of previously published documents, then that’s spam, and Google don’t want to waste time indexing yet another copy of data they already have.
Instead, Google want you to use AI to put new data together (new data meaning data and information in your prompt that wasn’t used before), to add in aspects of your own unique personal expertise and experience, as that is what is valuable to the human customers of Google.