Why is my recruiter always asking if I got divorced or not when I meet with him ?

Answer 1

Because whether or not you have dependents( and how many)  dictates whether you can enlist or not 

Answer 2

maybe he wants to go out with you

Answer 3

If you have sole custody of any children after divorce you would become a "single parent" and thus would be ineligible for enlistment. He's doing his job.