He is just trying to convince you that you're not worth the raise, and that you wouldn't get a better job somewhere else. He is wrong. Apply everywhere. If you don't have kids or a mortgage, just quit.

I was in a similar situation once. I got lucky because someone in our department, who was much stronger than I was, found a new job as a manager at a different company. Then a year later asked me to come work for him. That does not mean you have to wait to be lucky. Update your resume, don't try to wait until you have some new skill, just update it to wherever you are now, and start applying. Remember to ask for at least 80k.