in provenance, the impala is depicted as quite dirty and beat-up, scuffed up and covered in mud. this is not the typical image that comes to mind when you say a man loves his car. in later seasons too, the impala tends to look shiny and new, and dean is seen performing maintenance on it pretty regularly—at least, there are many scenes that show dean taking care of it, and there are also many scenes which touch on dean's possessiveness and care for his car.
this isn't the case in season 1. season 1 dean has a beat-up hand-me-down from his dad which he loves and admires but is still willing to let it get dirty and dented and scuffed.
in season 1, the impala represents john.
based on how john talks about the car in dead man's blood, he still has a semblance of ownership over it: john gave dean the car, but he still considers it "his" in the sense that he feels entitled to judge how dean cares for it. dean, too, doesn't argue with this. in season 3, dream dean even uses this against real dean to drag out his insecurities and his abysmal self-esteem:
both john and dean agree that the impala is john's car. this makes sense because the impala is also sam and dean's literal home, or the closest to home they've ever gotten.
you have a good "home is where the heart is" kind of connection here: the impala is home, and john is the impala—john is home, john is their father, john is the thing that connects sam and dean by blood. et cetera et cetera.
so if the impala represents john, then how dean treats the impala gives the audience a lovely visual metaphor for how dean feels about john. provenance is just one episode after something wicked, where dean is finally starting to extricate himself from his father. the entire season has followed dean as he experiences betrayal after betrayal from his father, and in shadow we see evidence that he doesn't actually believe that his father will come to protect them anymore—he's effectively given up on john as someone to rely on, and he's spent the whole season separating himself from john and attaching himself to sam instead. provenance gives a nice wink and nod at this by showing the state of the impala—dean is upset with john, their relationship is crumbling, and dean doesn't know how to repair it.
one episode later john remarks on the state of the car, and one episode later dean finally defies his father for seemingly the first time.
so when dean starts destroying the impala in everybody loves a clown, what dean is actually destroying is john.
he feels angry, upset, hurt, betrayed all over again. john is dead, and his final words to his son gave him an impossible task. dean takes the crowbar to the impala right after sam corners him into another conversation about john—this is an outpouring of his emotions about him, all concentrated on the last remaining symbol of his father.
but what i think is interesting is that sam doesn't see the impala this way.
sam sees the impala as dean. the symbolism here is very, very obvious. if sam gives up on the impala, then he's metaphorically giving up on dean. and sam refuses to let dean die, so he can't let the impala die, either. to sam, the impala is dean. which necessarily means that to sam, dean is his home, as well.
which is exactly what he just chose in the season 1 finale when he picked dean over his revenge. sam spent the entire season scared to "go home," and in devil's trap he finally returns for good to his home—to dean.
and in bloodlust, the impala is fixed, and she's shining like new. from this moment on, dean shows a rather pointed possessiveness over his car.
this is also the first time dean calls the impala "baby." this is the first thing that happens after dean destroyed it in the episode prior. the dissonance gives a sense of rebirth: something happened between dean destroying the impala and dean fixing it. something happened between dean using the impala as a stand-in for his father and dean calling it his baby.
in season 2, the impala no longer represents john. john is dead, and dean killed him. "home" is no longer centered around john; their father is no longer the thing that connects sam and dean. in devil's trap they chose each other, they chose codependency, they created a relationship between them that transcends the family structure they inherited from john. john is not part of this new relationship—it's just sam and dean now, and john is dead.
dean assimilates to sam's perspective when he rebuilds the impala: his car is now an extension of himself, and he is the home that sam chose. this is now his car, not john's; he is now sam's family, not john. and throughout the first half of season 2 dean struggles with this new responsibility and what that means for him—how their codependency should work, whether or not he should try to fill john's shoes, what "home" is supposed to look like for them without john in it.
i think it's an interesting way to depict dean's emotional shift across this stretch of episodes. seasons 1 and 2 especially do a lot of great work to depict john even in his physical absence, from allegorical substitutes to his haunting presence to this, representing him through the symbol of their literal home. noticing this makes me much more emotional about the impala's role in the story, because it's a physical manifestation of the effort dean put in to become sam's home and commit to their codependent relationship. he loves his car because it's his home, and his home is where sam and dean's hearts are.
