A lot of people don't understand the dynamics of what is really happening here.
NATO has a policy of not taking in members that are currently in a civil conflict. Which makes sense because then political parties in conflict could leverage NATO to settle their own disputes, and put NATO in a difficult position of picking sides. Not to mention countries who are a part of NATO need to demonstrate democratic agency and stability.
Ukraine has been in civil unrest for decades now, primarily because Russia infiltrated Ukrainian politics (with the help of a certain Paul Manafort...) to destabilize the country and create a separatist movement to drive it towards Russia. Ukraine has managed (in the past decade) to create new accountability laws and rout out corruption, defeating a lot of the bad actors and fighting back for its democratic sovereignty.
The Russian infiltration went from being political active to rebel terrorists and have been fighting Ukraine for a while now, hence delaying its membership with NATO. Recently, Ukraine has finally managed to almost totally destroy the rebels. Which is why Russia is terrified; with the rebels ousted, Ukraine can finally join NATO.
So while Zelensky does have a point (somewhat), he's also trying to thread the needle between quashing the Russian terrorists (and achieving a "relatively stable status") and Russia's oncoming invasion. It's like kicking out your abusive roommate, slamming the door, and demanding your local club quickly make you part of the peace-maker's association while he's still banging at the door. Which is very tricky for NATO to do, for obvious reasons (not least of all being nukes).
This is a very VERY summarized version of events, taking out a lot of nuances, details, context, intentions, and key people so take it with a huge grain of salt. But it's a general idea of why NATO is being cautious. Which, frankly, they should be.
