After 13yrs he shown up for our son graduation,asking to put his name on his birth certificate

After 13yrs he shown up to my son's graduation day,I didn't want na maging kontrabida because it's a special day for my son so I let him be present to that occasion.Then in the middle of the ceremony,he ask me if he can put his name to his son birth certificate.I ask him "for what?",he replied "sa mga insurance and as dependent sa work Niya .I told him that there's no need for that because our son doesn't need it.Tama ba mga mommy na tinanggihan ko?because we have our separate lives and in respect to our partner.he's giving 5k every 3mos for his son.all I want is to be a co-parent to our son pero hearing what he told his workmate (he even didn't admit na his fault or mistakes that we have a broken family but binabaliktad niya lahat to make him innocent).