(Assumed United States Jurisdiction)
If the client made the check out to him, then he paid you half. He would need your SSN or EIN (Tax ID) to show the payment on his taxes to you as a 1099 payout. If he were to not do this, it would appear he made the entire $6k and would owe tax on all of it. He's correct in wanting to claim the payout to you to decrease his tax liability.
You would need his SSN/EIN to show where your $3k came from. If he cut you a check, he paid you. The client did not pay you. He actually should issue you a 1099 form with his information on it.
If he's claiming you as an "employee" then he needs to issue a W2 to you for your taxes. And he's also on the hook for Unemployment, social security, etc, surrounding your employment position. It's doubtful he wants to claim you as an "employee". I suspect either you used that word incorrectly or he did.
If you both received money from the client, then you would both file taxes independently on the funds using the client's tax ID as an identifier of the income source.
As with all matters regarding taxes, you really should speak to a tax professional. While other freelancers may have some experience with similar matters, only tax professionals will be in a position to provide direct advice. I am not a tax professional.