Like many who answered, I'm no big fan of heights, and that was always a sore spot for me. Therefore, I set out to conquer that fear. I took up rock climbing!
No kidding, it worked. I'm still don't have a real love for being in high places, but by constantly facing it, I've managed to get over the sense of panic I once experienced. It didn't come all at once, though, and there wasn't a single "breakthrough moment" when the fear went away. Rather, I started off with very minor climbing challenges. Some were only a few feet, but I worked my way up, literally and figuratively. That's exactly what I suggest for you. Start off with "giant strides" that aren't all that giant. With little or no gear, do strides off the edge of the pool, and if that's too much, then stride from the ladder or steps at a pool. Progress to strides with limited gear, perhaps snorkel and mask, then snorkel, mask and fins. Work your way up--full gear, then from a low platform with gear. Always do exactly the same thing with a routine that you will follow every time. Do what these other divers have said and what your trainer said. Yes, it helps to look at the horizon. Also, it helps to visualize yourself doing giant strides SUCCESSFULLY (never visualize a dreaded disaster).
With some time and repeated practice, you'll face down that fear in no time and be ready for that 5 foot step off the M/V Fling or M/V Spree (both charters in the Gulf of Mexico with really TALL dive gates) in no time. Best wishes and welcome to the sport! Bless you.