Helping my son deal with his mental illness, drug addiction, and ultimately suicide.
I really have never felt like an adult, until my son moved in with me (I met him when he was 5 days old, and was kept from seeing him again until he moved in with me when was almost 17). Suddenly I had to deal with his medication, his appointments, keeping him out of trouble, learning to be a father of a 17 year old I did not know.
After his death the feeling stuck around for a while, but has slowly gone away over time. My last born child turned 18 earlier this year, and while that made me feel old, it did not make me feel like an adult. I even took him to register for college that, just feeling like an old kid.