Russia took most of its casualties in the second, 3rd and 4th week, when they were sitting like ducks waiting for resupply. Russians raced to Kiev without clearing the countryside. They got absolutely demolished in the 2nd, 3rd and 4th weeks by the Ukrainian ambush units still controlling the countryside.
And that's the Ukrainians winning the perception war.
The Russian losses are questionable. From an initial high, where the Ukrainians took them by surprise, it turned into attrition warfare. And it doesn't take a lot to push back a BTG, taking out a few tanks and IFVs seems to do the trick, but also doesn't result in large casualties.
In the initial days, they will going around assembling like idiots, but they changed their tactics over time. Recall that the "stuck" logistics chain did not suffer from much attacks. All we saw were pictures of stationary trucks and combat units. Do you think the Ukrainians would not have released images of major losses to the convoy? Also, a lot of the Russian losses we saw, particularly on roads, were a few trucks and combat units packed close to each other, probably when the Russians thought there won't be much fighting, but these did not experience complete destruction either.
Russians are moving forward like snails while retreating (running away) hundreds of kilometres. I am surprised that you used Izium as an example of Russian advance

.
In Izyum, Russians are fighting for more than 1.5 month and they can't move forward any significant way. Russians advanced a grant tottal of 5 kilometers south of Izium in 1 whole month. In that process, they lost thousand of troops.
Map of Izium front April 18th, 2022
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Map of Izium front 1 month after (May 17th). Russians made an advance of 5km in a whole month.
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Incremental gains are still gains. But what about Ukrainian losses? Because that accrues over time.
You start off with initial gains and that slowly builds up, just like compound interest. Now the question is how long does it have to compound before they achieve a breakthrough.
Ukrainians already stopped Russian offensive. Or better, they counter attacked and recaptured ( Or as Russians call it, glorious retreat) thousands of square kilometres. "
Retreating from areas where offensive is unnecessary at this time?"



. Did you mean areas where Russian offensive failed and got absolutely demolished?
This is again what perception war does. What did Ukraine lose during that time? How much did Russia lose relative to Ukraine? The Russians may have backed out, but retreating means the Ukrainians would advance and then thin out over a larger area, then the Russians can go back in again.
The Russians don't have numbers, so they need to concentrate in one operational area at a time. And as the operational area expands, other areas come into focus.
Russian attack came to a halt in all fronts and they are incapable of concentrating forces for an attack, let alone conduct a successful offensive.
At this point of war, daily Russian loss is similar to Ukranian losses or even higher. Ukrainian Artillery units proven to be far more effective than Russian one.
Ukraine is fighting a total war with full mobilisation. They can afford to loose more troops, Russia cannot. And Russia not asking for ceasefire doesn't mean Russia is winning.
If there's no change in tactics from the Russian side, then it means the tactics they are currently using are working.
Temporary ceasefire favours Ukraine,that's why Russia not accepting it. Temporary ceasefire means more NATO trained troops and weapons, more repaired bridges and more time to bring heavy weapons to east from the west. Russia gain nothing from a ceasefire, so they obviously rejecting it.
We are not talking about a ceasefire, we are talking about stopping the war itself. The point is Russia's demands have not changed based on the media's perception of the ground situation.