What exactly is that assertion even based on?
People talk like it is some kind of a definite fact, but there is no reference to any particular source or a universal explanation of how this was deduced.
well for starters the fact that there is no record of him saying that
Just before the war, he said he was not going to invade. Then he did it anyway. His words are meaningless. His actions are what counts. And he obviously did try to take Kyiv. There were paradrops intended to take Kyiv in hours, even. There was a push by more forces to take Kyiv in days. It all failed because they encountered far more serious resistance than they expected, and it turned out they lacked the supplies for a longer operation, and couldn't get those supplies organised in the face Ukrainian defense specifically targeting Russian supply lines. Eventually they couldn't make any progress and withdrew. Though not before murdering lots of civilians in Boucha.
https://www.theguardian.com/world/2014/may/02/ukraine-dead-o...
that started after both sides hurled molotov cocktails at each other?
The world is complicated, yes, but your comment reducing this to "one side burned the other side alive" is disingenuous at best.
Ukraine is smaller than Russia, but by no means a small country. Ukraine has 40 million people and is far more motivated to fight than Russia is. Russians really have nothing to win here; it's just about Putin's pride. Meanwhile Ukrainians are fighting for their lives, their country, and the future of their children. These are powerful motivators, and go a long way towards explaining Ukraine's unwavering morale in the face of overwhelming odds.
Ukraine also fights much smarter. Russia uses very primitive tactics: use massive artillery to flatten entire cities, move infantry in, and if they get killed, flatten the place with artillery again. And then they ran low on artillery ammunition, not to mention that many of their barrels have been so overused they can't shoot straight anymore, so now they've resorted to human wave attacks. Ukrainian defenders of Bakhmut have described wave after wave of Russian attackers crawling over the dead bodies of their dead comrades only to get gunned down too. There's no sophistication at all, and coordination is often poor.
Meanwhile Ukraine with its more limited resources executes very smart attacks. Most of the time they target Russian supply lines to make it harder for Russia to fight. But sometimes they've undermined Russian positions so much that they can suddenly grab an enormous swath of territory, like they did east of Kharkiv and west of Kherson.
I frankly don't see how Ukraine can lose this. In some ways they have already won. Although of course it really depends on how you define victory and loss here; both sides have lost a lot, and any end result where Putin is in a position where he can try again later, means that the war for Ukraine is not really over.