Why is RSA private exponent much larger than RSA public exponent?
Is my guess correct?


Not really; we don't go out of our way to deliberately slow down the decryption operation.  Instead, things are set up that way because that's what's needed for security.


It turns out that if $d$ is small (e.g. less than a fourth of the size of $n$), and we tell people what the corresponding $e$ is, it turns out they can factor $n$ efficiently.  Hence, $d$ needs to be large to ensure security.
There's no similar issue for $e$; telling a people a small $e$ doesn't help them factor $n$ (or otherwise break RSA).  Hence, there's no reason not to select a small value (and make the encryption operation faster).