The Budapest Memorandum didn't offer security guarantees, it offered certain assurances to the nations concerned when they agreed to give up nuclear weapons on their territories.
Article four is most relevant. The signatories agreed to Seek immediate Security Council action to provide assistance to Belarus, Kazakhstan or Ukraine if they "should become a victim of an act of aggression or an object of a threat of aggression in which nuclear weapons are used". That is a long way from a security guarantee and even further from any kind of mutual defence pact.
It's a worthless piece of paper, torn up by the Russian Federation.
The current problem is that Putin has made a gamble and is losing. When a gambler has already lost so much that he will go bankrupt unless he can turn it around, the logical thing for him to do is to continue upping the stakes. This is the desperate opponent the West may now face. The trick is to give Putin a way out without humiliating him and Russia, whilst being seen to save Ukraine's territorial integrity. It will be a difficult trick to pull off, and the stakes are very high. If Putin is to accept a negotiated defeat, he will require a fig leaf to hide the reality that he has failed to subdue Ukraine.