Strategically, the issue here is the potential for escalation and in particular the threat of nuclear escalation. A conventional war between two nuclear armed powers has generally unacceptable escalation risks. The key thing to understand here is that real war is not like in video games where one can clearly see what units the enemy is using and where firing a nuclear weapon is accompanied by a big loud siren everyone can hear. In practice, many of the same systems NATO uses for conventional warfare can also potentially be used to deliver nuclear weapons – the Tomahawk cruise missile was designed to carry nuclear payloads, for instance, and while those particular nuclear weapons have been retired (the payloads, not the tomahawk), the capability to mount them still exists (and if you were a Russian commander, would you assume the United States was entirely honest about the nuclear capabilities of its cruise missiles?).
Moreover, as Caitlin Talmadge describes in the Taiwan/China context here, the very nature of the way modern militaries fight means that efforts by a NATO military to shield its own ground troops or fighters from enemy fire – essential for their survival – would involve strikes in Russia which might be effectively indistinguishable to Russian eyes from efforts to blind Russian eyes in preparation for a NATO nuclear first-strike. Some of those strikes would be using dual-purpose weapon-systems and the entire point of NATO doctrine in these sorts of instances is to paralyze and confuse enemy command and control, which of course makes a mistake more likely. The same would of course be true in the other direction, so both the tired, confused Russian commanders and the tired, confused NATO commanders would be squinting at their intelligence reports always wondering if the next missile might be the beginning of a nuclear war. The potential for catastrophic miscalculation leading to a nuclear exchange is far, far too high (and that is before one accounts for what one side in that fight might do if it became clear they were losing the conventional war but might salvage the issue by upgrading it to a ‘limited’ nuclear war).