Please help me understand why RNA vaccines do not "change your RNA"

My analogy from this thread in April is similar to yours:

Here’s an analogy: DNA is a printing press. mRNA is a page of written instructions printed from that press. The ribosome is the construction worker handed those instructions. The mRNA vaccine means that you take pages of instructions printed on someone else’s press and hand them to the construction worker, who then builds the spike protein. But the page of written instructions do not and can not land of top of the printing press and modify it any more than a real piece of paper laid on top of a real printing press can rebuild it. The only situation in which the prospect isn’t transparently idiotic on its face is for people with no understanding of genetics.

The main concern about your version is that you say just “RNA”. There are multiple types and you need to specify that it is mRNA, messenger RNA.