Hello. My name is Michael. I can help you with your question.
The signal is obviously strong enough so it has to be related to configuration of the network - most likely security. Is your router using "MAC address filtering"? This filters devices by their hardware addresses. And this is enabled on many Apple network products by default. If you find that you do have that enabled on your router/airport, just disable MAC address filtering, and you should be ok. The alternative is to add the MAC address of the printer, but it really doesn't provide any additional security - it's a very old way of implementing security and can easily be spoofed today, making it useless.