By default, Amazon EC2 instances have a form of "IP address spoofing" applied. So traffic to/from an EC2 instance must have the address of that instance in the packet. That means it can't be used as a router or a VPN gateway; Amazon blocks this traffic. This is called a "SourceDestCheck" in the Amazon documentation.
So you need to tell Amazon to disable this. From the GUI this can be done by navigating to EC2/Instances, selecting the instance you want, then Actions/Change SourceDest Check.
From the CLI it can be done with the `aws ec2 modify-instance-attribute --no-source-dest-check` options.
Of course your security groups also need to allow this traffic!