bahkmut for the russians means they can threaten Kramatorsk and Sloviansk. Ukraine staying there means they can inflict heavy attrition to Russian forces and protect Kramatorsk and Sloviansk. It really isn't that important in terms of location, but its become a propaganda war.
The Russians have hyped it up and now they have to take or they do look stupid (which is a really bad way to wage a war) and they would have to take it at some point anyway.
The Ukranians don't really want to lose it for propaganda reasons, they can inflict heavy damage to whatever russia chucks in there and they are sort of saying 'we could go back to our next postions, and then if that goes badly go back to our next positions and eventually go back to kyiv...but why bother with going all the way back to kyiv why not make out stand here?'