Ukraine would never do that unless forced to under duress or coercion? So it becomes a chicken or egg problem, does Russia present a security threat to Ukraine because of Russian demands for neutrality (OR ELSE bad things happen!), or does Russia present a security threat to Ukraine because of historical domination by Soviet Union and Putin lamenting the loss of Soviet Union? That is the chicken or egg problem, which came first?
Just as Putin demands Ukrainians' pledge to never join NATO be codified in a legally-binding treaty and aspirations removed from Ukrainian Constitution, I would expect Ukraine to demand Russia 'ought not be security threat' to be codified in a legally-binding Non-Aggression Pact. Fair enough right? If Russia cannot trust NATO's short-term promises and wants permanent long-term solutions, then Ukraine can similar expect permanent long-term security guarantees from Russia to be 'ought not be security threat', which does not appeared to be offered? Has Russia offered (permanent) security assurances to accompany it's demands for neutrality?
You said it yourself, Putin demands a binding written agreement that ensures Ukraine's neutrality. Neutrality means not joining military alliances against each other and allowing own territory to be used for attacking each other.
The very nature of a neutrality pact is that it binds
both parties. This has never been an issue of dispute for Putin.
In case you forget, it takes two to sign a treaty, so Russia would also be bound to not engage in acts that violate Ukraine's neutrality and likewise for Ukraine to not harm or allow itself be used to harm Russian interests, which has always been Putin's position, which incidentally makes your questioning of what assurances Russia would give to Ukraine's security seem odd, since that would be a non-issue with a neutrality pact as explained.
That being said, whether Ukraine thinks she should make herself neutral in the first place is a different matter, and as I said in the beginning I'm not delving into the right and wrong of it.
Only that if Ukraine doesn't think she should be neutral because she sees Russia as a threat, that's entirely her right, just as it is Russia's right to seeing Ukraine as a threat as a result.