That depends on what you’re referring to. Quick caveat, I’m not an expert in regenerative biology, but I have studied it somewhat.

The trick is that the healing that you’re referring to, it’s not really healing in the way that you’re imagining it. The skin doesn’t really quite grow back in the same way. Instead, there’s more collagen than there normally would be (we would then call that scar tissue). In essence, we’re not really healing, our bodies are just doing a patchwork fix. The presumed reason is that our bodies figure that it’s not going to cause any problems before we die from other causes. This is really quite true of other tissues as well. The liver is known to be able to grow back, but if you look at the microstructures, the regrown stuff is missing a lot of the nuances that the original had. Our bodies expect us to live 70-ish years, and so they don’t care about anything that could happen after that.

In order to truly, really regenerate, you’ll need stem cells. Some animals are remarkably good at keeping around stem cells and regenerating, but somewhere along the evolutionary line, mammals lost the ability to use stem cells. It’s still an ongoing area of research about why this happened and whether we can generate stem cells in the lab and whether we can manipulate stem cells to our benefit. It should also be pointed out though that, by its intrinsic nature, stem cells divide and don’t specialize into any roles, so it’s very easy for them to go cancerous. In the few spots where mammals do keep stem cells around, their division is very tightly controlled, and even then they are the source of the most common cancers in humans