How come I can't FaceTime my boyfriend?

Here is a troubleshooting support document you can try. Get help if you can't make or receive FaceTime calls on your iPhone, iPad, or iPod touch - Apple Support

Are you on wi-fi, or does your carrier support FaceTime over cellular? So even if you open FaceTime, then search for his name there, it does not come up? If you open FaceTime after he has called you on FaceTime, which you said he could do, does it list him and his contact information there? If you tap on it to call him from there what happens?

What happens when you try? If you open FaceTime, then search for your boyfriend's contact card, and then click on his phone number, will it not connect? Did he used to have something other than an iPhone in the past that you have been communicating with?