Why can't you decrypt an encrypted message with just the public key?
I stumbled onto this great write up by Cloudflare a while ago as I was trying to understand Elliptic Curve Crypto better. It however starts of with some background on Public Key Cryptography followed by a detailed explanation and example of RSA key pair genaration AND how those keys (smallish primes) are used to encrypt a basic message. I suspect you will find that example answers some of your questions.

Specifically refer to the sections titled "The dawn of public key cryptography" and "A toy RSA algorithm".

All subsequent sections deal with ECC and go into a fair amount of detail (a great article on the whole).

Edit: If you tinker with the values in the example it should illustrate why the mathematics would not allow you to decrypt a message using the public key.