If you are still married you must file either married filing jointly (if you both agree) or married filing separately. When filing separately, each spouse must put the other spouse's SSN on their return, if you need his SSN, he needs yours. This is not complicated and there is no reason to refuse except to be a jerk.
If your spouse refuses, you must file by mail, you can't e-file. You will need to use a fake SSN to get turbotax to print the return, try 999-88-1234. After the return is printed, use some whiteout to cover the fake SSN. Attach a written explanation that your spouse refuses to give you their SSN, and provide the spouse's full name, birthdate, and current address. Sign and mail your return with the attachment.
Note that if you provide care in your home for a qualifying child dependent, you may be able to file as head of household, in which case you do not need your spouse's SSN.
