Horses tend to prefer long spots when they're younger/greener/less experienced. In general, it comes from the "brave chicken" mentality that's desirable in a horse we ride over fences: brave enough to want to jump the fence, chicken enough not to want to touch it. Your horse needs to learn to jump pushing off on its hind end, not hurling itself over on its front end, and to use itself efficiently and economically. The way to teach this is, as previously said flatwork and gymnastics. I wouldn't even be jumping your horse over singles fences right now - just grids and gymnastics.
Part of the flatwork you need is to be able to shorten and lengthen the canter at will. Not only does this develop your sense of pace and balance, it gives your horse the tools to make a bad spot work. Once you can reliably produce three distinct speeds at the canter, do this exercise. Lay two groundpoles down a long side of an arena exactly 96 feet apart. Canter over them until your horse canters over the poles in an even stride, with each pole in the center of the stride. This is a regular 7 stride line. Count the strides until your sure which are the "pole" strides and which are the line strides. Do this in both directions until you can nail 7 regular strides and canter over the pole without fuss. Then work on cantering it in 8 steady strides from your shortened canter; then 6 from a forward canter.
Once you've truly mastered this exercise, you difficulties seeing distances will be about gone, because you will have mastered pace. To put the finishing touches, do the same exercise with a line of verticals.
Another good exercise which I like to use *sparingly* and after you've mastered the pace exercise. Set up a single fence at least 2' 6" and use either field marking spray paint or stall lime to mark a "zone" on the ground for the correct take off and correct landing.
Have someone knowledgable on the ground, preferably an instructor watch you jump the single fence. Tell them if you thought the spot was short, long or just right. Then have them point out your take off and landing spots and see where they fall within the marked zones.
The reason I say to use this exercise sparingly and only after mastering pace is that it can encourage looking down in the approach, a serious flaw that encourages chipping in by the horse.
And yes, horses can be trained to see their own distances. It takes competent handling and a lot of mileage. Once they get there, they are priceless. I've seen a good horse take the bit and make the correct 7 work when the kid on its back was sitting down and holding for the steady 8.