What an uneducated fool, only the custodial parent can legally claim the child so don't let him bully you. The IRS definition of custodial parent is with whom the child live for more than 1/2 the year so keep careful records on a calendar and don't let the child spend more nights with him then with you.
If you both claim the child the first can be efiled and the second will be rejected requiring that person to mail the return in. Then the IRS will sort out who gets to claim the child so be prepared to support your right to claim. Read the dependent and the separated parents rules in the IRS pub 501: http://www.irs.gov/pub/irs-pdf/p501.pdf