Why can't you decrypt an encrypted message with just the public key? How does asymmetric crypto work?
For example, if you use PGP in emails, you generate a private key that is known only to you and a public key, which is available to everyone.
Is there a simple way to explain, why you need a private key and why no one can decrypt the message with just the public key?
I think of an explanation like for example with prime numbers:

If you multiply two large prime numbers, you get a huge non-prime number with only two (large) prime factors.
Factoring that number is a non-trivial operation, and that fact is the source of a lot of Cryptographic algorithms. (See one-way functions for more information.)
The product of the two prime numbers can be used as a public key
The primes themselves as a private key. So the private key is the knowledge of two very large prime numbers

for easy understanding lets take the simple example (very large) prime numbers: 3 and 5:

private key: the knowlege of 3 and 5
the public key is just those numbers multiplied: 15
you cannot find out 3 and 5, so the message encrypted with 15 is ...

Here is a quite good explanation already, but it is not clear enough:
Is there an intuitive explanation as to why only the private key can decrypt a message encrypted with the public key?
Can you please add an example with those numbers?
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.