I know there are questions that might sound similar, but this is a completely different one. Firstly, I am using the word extending and not expanding. Secondly, the question is limited to a time period long before 2008 and even before Putin came to power.
At the beginning of the 1990s, the Cold War was officially over, there was no Warsaw Pact and even no USSR was there to threaten NATO. The new Russian government was relative pro-Western, the most pro-Western government in Russia ever. There was no anti-Western propaganda in Russian media, sometimes even the opposite was the case. Thus, no real threat from Russia was expected at that time. It was also clear that extending NATO would change the situation and bring back confrontation. Some people in the Clinton Administration convinced him to postpone the NATO extension at least until after the presidential election in Russia in order to prevent anti-Western candidate from winning. While the arguments against that extension are clear, which ones were for supporting it? People like New York Democrat Daniel Patrick Moynihan and George Kennan have warned that extension of NATO can have bad cosequences.
In 1997, even before Americans learned about Vladimir Putin, 50 former senators wrote a letter to President Bill Clinton against the expansion of the alliance, calling it a political mistake of "historic proportions."
Richard Nixon confirmed that the new Russian government was relative pro-Western:
Yeltsin is the most pro-Western leader in the history of Russia...
Whatever its shortcomings, the alternative to the new despotism will
be much worse
At least acording to an article in german press there was a promis to not extend NATO to the east as can be seen here. At least Russia sees the document mentioned in that article as such promis.
So here a reference to a credible source about the claim that extending NATO would change the situation and bring back confrontation.
The question is refering only to reasons from core NATO countries, specially USA, and not the new members from East Europe, as their reasons are very clear.
Here some references about a discusion which was led in the 1990s in US:
https://newrepublic.com/article/165562/nato-critics-predicted-russia-putin-belligerence-ukraine
https://www.theguardian.com/commentisfree/2022/feb/28/nato-expansion-war-russia-ukraine
https://www.rferl.org/a/1088215.html
https://www.vox.com/22900113/nato-ukraine-russia-crisis-clinton-expansion
https://patrickarmstrong.ca/2016/02/14/george-kennan-on-nato-expansion
https://www.moonofalabama.org/2014/03/george-f-kennans-prediction-on-nato-expansion-was-right.html
