The main reason for this failure is that the locations SPSS tries to use are not writeable. You might try starting SPSS in Admin mode and then doing the install.
Another solution would be to create a directory where you know you have write permission and then create an environment variable like this example
SPSS_EXTENSIONS_PATH=c:\extensions
SPSS will then put that first on the list of locations to try. After you create it, restart SPSS before trying it as environment variables are read only on process startup.
Running SHOW EXT will display the locations where SPSS would try to install them,