Your relationship with your client might have nothing to do with his appreciation of your services. There's no point in overanalizing the reasons why your client wants to print elsewhere unless you actually see the print quote he was offered.
It's not rare some printers offer free graphic design services to their clients (no matter how amateur it can sometimes be) and that's hard to compete with that for a designer or a reseller.
So here are your options:
1) Sell the files. That's how you compensate for the "loss of income". The price of the file should be high enough to make the client consider printing with you instead. Offer a printing quote for their project as well. If the client wants editable files, there's answers on this stack on how to set your prices. If you aren't 100% happy to sell the files, simply set a very high price and see.
2) Refuse to give the files and hope the client will decide to print with you because of that coercive technique (eg. "you print with me or you don't get any files"). You'll either get something out of this or nothing at all, and risk to never see that client again. That bet is up to you and only you know the value of the files and potential printing contracts related to your question.
Unless the project you are talking about has a very high value, don't make the mistake of thinking your client absolutely need these files. If you make things complicated for your client simply because you are not happy to see him try another printer, he might as well end up simply choosing to redesign the whole project with another designer and print somewhere else anyway. Sometimes selling the files and letting go a bit is the best way to see that client again in the future. You never know, your client could end up having a terribly bad experience/results with the other printer and come back to you.
The client could be lying too and in fact, your prices are way too high and there's no way he thinks you can match that quote. That's why it's also a good idea in your situation to offer a printing quote too and show you're opened to negotiate.