That might have been how it worked out if Ukraine successfully fought a war of attrition and Russia fought a war for territory, but it was the exact opposite.

To take Bakhmut as an example, Ukraine kept feeding men into cauldrons long after they should have cut their losses because they had orders to make a stand and fight to the last for every inch of territory. This is where the phrase "meat grinder" originated - it described Russia's plan for capitalizing upon those orders.

Ukraine ended up suffering vastly worse casualties than Russia did as a result - their troops spent most of their time surrounded on 3 sides by a force with overwhelming artillery superiority. The Ukrainian soldiers fed into these cauldrons often died within hours from an artillery strike, usually without even seeing a Russian soldier. Russia tried to keep this process going for as long as possible.

Hence meat grinder.

This pattern of Ukraine prioritizing territorial gains over lives and falling into traps sprung by Russia as a result has been repeated elsewhere across the front line too, and is symptomatic of the failure of the counteroffensive.