Why your back aches:
Another reason people give up cycling is because their back starts hurting. They might already have had back injuries, and cycling might be aggravating that problem for them. There are a few bicycle adjustments that can be made to avoid having any back associated pains when riding a bike.
Lower back pain on the bike comes from having too long a top tube on the frame to where the rider is having to overstretch to reach the handlebars. It can also come from having a poor saddle positioning where the saddle might be tilted inward or outward, instead of being a flat surface for the rear end to rest on. The saddle should only be moved forward and backward, never tilted up or down. There are saddle designs, like ones made by Vetta or Selle San Marco Concor, where the end of the saddle will have a small lip that flips upward, intending to catch the rider's rear end and keep it there. These kind of designs call for tilting the saddle slightly. Most newer saddles are no longer designed this way.
Upper back and neck pains are associated with stem length and handlebar width. Most people who started riding with a new road bike are conditioned to having a sloping top tube, a riser threadless stem, and at least 42cm wide handlebars. Going to a traditional diamond framed bicycle with a flat top tube, quill stem and 40cm handlebars might make things uncomfortable at first. A quill stem forces the rider to find their comfort zone much faster than a riser them. That is because there are only mere centimeters that can be pulled out of the head tube before the height limit is reached. Quill stems force a rider to adopt a racing position much quicker because the rider has to reach below the top tube to grab the drops of the handlebars. This stretches the back in a way that might seem unnatural at first. The discomfort usually goes away in a few months. If it doesn't, then maybe it's time to look at some other causes, such as the width of the handlebars.
Why are handlebars wider nowadays? Because we are bigger than our parents were in their prime, and our parents who are still riding have become old and fat. Wider handlebars allow the rider to breathe better, but also affect aerodynamics and top speed. The key to choosing handlebars for a road bike is not choosing the widest ones first. Choose the handlebar that will allow you to breathe efficiently while still allowing you to adopt a racier position.
Here's my rule of thumb on handlebar width. I choose the handlebars according to my tuxedo size. My chest size for a dress suit is between 40 and 42 inches. 44 inch suits will start to feel baggy on me. The same goes with handlebars. You can get the "sport" fit at 40cm, the "relaxed" fit at 42cm, or the old man "frumpy" fit at 44cm. Keep in mind, at 44cm speed gets taken out of the equation, as average speed can actually go down by a couple of miles an hour.
For some older riders or riders getting into cycling with previous injuries, these adjustments might not be enough. Some might have to buy special stem adapters to achieve a more upright riding position. Eventually, this leads to the stereotype where all recumbent riders are old guys with white beards. But road biking isn't for everyone, and some people no matter how hard they try just can't get a road bike to work for them. That's fine, that is why there are different bikes for different people.