Says the Mishnah: any type of korban (offering) that became invalidated before they were skinned, the skins do not go to the Kohanim (priests), but just like the animal flesh is burned in a special spot in the Beit HaMikdash, also with that the skins that became disqualified, it's one entity, so the whole thing is burned. But if the invalidation happened after they were skinned, then the skins do go to the Kohanim, only the meat is burned in that special spot for pasul korbanot (invalid offerings). But the question becomes: what happens if after the skinning we found out that retroactively it was problematic? In other words, let's say the skinning of the animal happened and then we find out that the animal was a terefa (it had a blemish internally and it was going to die). What do we do with the skins at that point? So it's unresolved at this point of the Mishnah.
So Rabbi Chanina is going to give us an answer for that. The person who was in charge of the Kohanim at that point in time, he said: In all my days that I was serving in the Beit HaMikdash, I never saw a detached skin of an invalid korban being taken out of the Mikdash to the Beit HaSereifa (the place of burning). In other words, in that case that we just brought up where it was found out later on that it was a terefa, that would have been a common occurrence enough to say that we're going to take the skins and burn it, even though they've been removed from the animal. If that was true and he says he never saw it happen, so therefore our case of an animal that was found out to be a terefa, it must be that the Kohanim were allowed to partake of those skins and there was no need to burn them.
Amar (said) Rabbi Akiva. Rabbi Akiva said it about that statement, says Rabbi Akiva about the statement of Rabbi Chanina, that we learn that if one skins a blemished bechor and it's found to be a terefa, that the Kohanim are allowed to benefit from the skins. The bechor is sacred from birth; it has to be given to a Kohen (priest). The Kohen then brings that bechor as a korban, but if it became blemished and you cannot offer it on the mizbeach (altar), the Torah allows the Kohen to eat it, but he slaughters it and eats it as ordinary meat. And in that case he's allowed to use the skins, but if it dies without slaughter or if he slaughters it and he finds it to be a terefa, then he's not allowed to eat the meat, obviously because it's considered to be unkosher, but also with that the skins become forbidden and they also both have to be burned.
But what happens if the Kohen did not discover the blemished bechor was a terefa until after the shechita (after the slaughtering) happened? What Rabbi Akiva says, we can learn from the statement of Rabbi Chanina is that just like Rabbi Chanina tells us that when we have a situation of a korban that it was found to be a terefa, if the finding only happened after the animal was skinned, the Kohanim are allowed to benefit from the skins. So we learn that as well for the case of the bechor that became blemished: if the terefa aspect was discovered only after the skinning of that slaughtered animal, we say the Kohanim would be allowed to benefit from the skins as if everything had been valid until that point in time.
But the Rabbis over here, they say we have not seen; it's not a proof. Just because Rabbi Chanina never saw a skin that was detached being burned doesn't mean that never happened. Maybe they were using the Beit HaMikdash where they never found a case of a korban to be a terefa after it was skinned, or maybe there was just that was the situation at that time. Maybe he didn't see it, maybe he looked away in some way.
So the Chachamim (Rabbis) said you can't bring a proof from the fact that he didn't see it. Ela yotze leBeit HaSereifa (rather even if the korban was found to be invalid after the skinning was done in that case as well it's taken out to the Beit HaSereifa to the place of burning both the meat and the skins), since we know now that the korban was invalid while it was still attached. We take it all out, we take out the skins as well, and the Kohanim are not allowed to take them; they're not allowed to be given the skins.