It was supposed to be just a regular task, another mission to complete. Yes, you knew they were dangerous. Yes, you went there fully aware of what might happen. Except neither you nor Annabeth thought it could be this bad.
You held one hand on the cliff and the other was wrapped around your girlfriend's wrist. You ran after her because you would never, ever let her fall there alone. you promised Annabeth you wouldn't leave her again, so you won't - simple as that.
Annabeth was afraid, it wasn't the first time but it wasn't something that happened to her often... she looked at you and saw that in a moment you would both fall into the abyss
"you can let me go baby, I can handle it"
of course I can't handle it without her
and then you couldn't stand it. you let go of the cliff and wrapped your arms around the girl mid-flight to protect her from the inevitable fall.
"im not letting you go again Annie"
and then you felt your body hit the ground