Recently watched this with my kids after not seeing it since being a kid myself. My pet theory is that it’s about coping with the death of a grandparent. When the scientists take E.T. away and hook him up to all the machines, it’s like the experience of seeing grandma or grandpa in intensive care with tubes, ventilators, etc. We see things through the kid’s eyes and there is a vague sense that the scientists are supposed to be trying to keep E.T. alive, but it looks like they are killing him.

In the end, the beloved companion E.T. goes up into the sky but says he will always be with Elliot in a sense (my memories of this part are pretty vague, but I think there was some message along these lines). Maybe this is just my personal experience, but it really brought back memories of going to see my grandparents in hospitals that were kind of threatening to me as a kid, and the idea that your relative is up in heaven now.