First, maybe you may or may not have the legal reason to fire this employee on the state law.
But, on the common ethic, you have every right to fire him.
There could be a lot of reason, which can make his firing possible, if the state law doesn't allow it for you.
He knows it probably also very well. But, you said, it is his first workplace, so he probably can't really imagine his first switch. He needs a little bit of "support" to make this decision, this is what you should give him.
You can have any "reasoning": the company doesn't have money for his project any more, somebody needs to be fired because of the financial state of your company, etc. And, of course: although you are very satisfied with his work, unfortunately you see that his role/skills are incompatible to your business model. Or any similar.
Do this surprisingly, without any foreshadow! For example, I've seen once a company, where the boss fired a group of developers on the following way:
- He called them to a meeting into his office.
- While they were going to him, he called the system administrator and asked to deactive all of their access to the company network.
- In the office he waited them with their letter of termination.
This is what you should extend by a secretly made backup of your whole network, before the firing. It will be useful if there is a already a backdoor in your system, on this backup you will have at least chance to find it.
You can't avoid all of the risks. It is your decision, if you accept it, or you try to give them further time. In your place, I wouldn't give: if an employee can do this to you, you simply can't let him in their place.