piping stdout of cat to kill's stdin

If I have the pid of some process stored in a text file, let's call it program.pid, and I want to end that process via the kill command, how come I can't do this:

bash:$ cat program.pid | kill

But if cat program.pid, and just type the output into the kill command, it works and I stop the process.  Why can't I pipe the output from cat to kill?

>>1-9999

You all fail, faggots