My apologies for getting back to you so slowly. You asked a good question and deserve an honest answer.
Why are the Ukrainians fighting for the regime in Kiev? From what I have heard, they are not. They are fighting for their homes. If someone kicks in your door and you have the opportunity to fight, what would you do? I know what Ukrainians would do. In fact, I don't just 'know' it: we can see it in the war.
They are fighting for their own culture. Ukrainians consume Russophonic media and what is said on TV? The 'popular' shows are saying the Ukrainians do not have a distinct culture or language. Even when blocked by Kiev, the TV shows are online. Those shows may help hype up the Russians, but it also enrages Ukrainians.
The Ukrainians see their future in Brussels, not Moscow. Ukrainians see Moscow as denying their precieved path to a better future.
Finally, Ukrainians are fighting because they feel betrayed. Russia was their brother country. Russia promised to respect the Ukrainian borders. So many Ukrainians are intermarried with Russian families. From the Ukrainian point of view, 2014 and even more so now, this is the Biblical story of Cain and Abel, the so-called first murder where a jealous brother killed another. Except in this version, Cain has not succeeded in killing Abel and now Ukrainians have the wrath of god burning within them.
That rage I've brought up several times. That burning rage is enough to power this war for years. I cannot highlight this enough.
Is it about Kiev? No, but Zelensky has been doing a fantastic job of winning the info war. Ukrainians are far too cynical to call him Churchillian[1], but you might still sniff a whiff of the proverbial cigar smoke all the same. The longer the war goes on and the more successful Ukraine is, the stronger the parallel will be seen.
So, predictions!
The Ukrainians will take the right bank of the Dniepr and the city of Kherson by the end of November, maybe even the end of October.
The Ukrainians will push into Lugansk to flank Kreminna by going for Svatove and Staroblisk. This cuts the railways and supply from the north. They will continue east to Bilovodosk and then swing south towards Lugansk, cutting off the rail logistics as they go.
I would not expect a Zaporizhia offensive until Kherson is secured, troops are rested and moved into position. This would probably be a winter offensive if it happens.
After that all depends if the Russians can get their shbt together.
1. Note: the brits threw Churchill out when they grew tired of him. He was actually a real nasty piece of work himself. I expect the Ukrainians will toss Zelensky out when they are tired of him as well.
